Log in

Relevant bibliographies by topics / Group algebras; Symmetry / Journal articles

To see the other types of publications on this topic, follow the link: Group algebras; Symmetry.

Journal articles on the topic 'Group algebras; Symmetry'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Group algebras; Symmetry.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Skalski, Adam, and Piotr M. Sołtan. "Projective limits of quantum symmetry groups and the doubling construction for Hopf algebras." Infinite Dimensional Analysis, Quantum Probability and Related Topics 17, no. 02 (May 28, 2014): 1450012. http://dx.doi.org/10.1142/s021902571450012x.

Full text

Abstract:

The quantum symmetry group of the inductive limit of C*-algebras equipped with orthogonal filtrations is shown to be the projective limit of the quantum symmetry groups of the C*-algebras appearing in the sequence. Some explicit examples of such projective limits are studied, including the case of quantum symmetry groups of the duals of finite symmetric groups, which do not fit directly into the framework of the main theorem and require further specific study. The investigations reveal a deep connection between quantum symmetry groups of discrete group duals and the doubling construction for Hopf algebras.

APA, Harvard, Vancouver, ISO, and other styles

2

Rong, Shu-Jun. "New Partial Symmetries from Group Algebras for Lepton Mixing." Advances in High Energy Physics 2020 (February 8, 2020): 1–8. http://dx.doi.org/10.1155/2020/3967605.

Full text

Abstract:

Recent stringent experiment data of neutrino oscillations induces partial symmetries such as Z2 and Z2×CP to derive lepton mixing patterns. New partial symmetries expressed with elements of group algebras are studied. A specific lepton mixing pattern could correspond to a set of equivalent elements of a group algebra. The transformation which interchanges the elements could express a residual CP symmetry. Lepton mixing matrices from S3 group algebras are of the trimaximal form with the μ−τ reflection symmetry. Accordingly, elements of S3 group algebras are equivalent to Z2×CP. Comments on S4 group algebras are given. The predictions of Z2×CP broken from the group S4 with the generalized CP symmetry are also obtained from elements of S4 group algebras.

APA, Harvard, Vancouver, ISO, and other styles

3

Walker, Martin. "SU(2) × SU(2) Algebras and the Lorentz Group O(3,3)." Symmetry 12, no. 5 (May 15, 2020): 817. http://dx.doi.org/10.3390/sym12050817.

Full text

Abstract:

The Lie algebra of the Lorentz group O(3,3) admits two types of SU(2) × SU(2) subalgebras: a standard form based on spatial rotation generators and a second form based on temporal rotation generators. The units of measurement for the conserved quantity due to invariance under temporal rotations are investigated and found to be the same units of measure as the Planck constant. The breaking of time reversal symmetry is considered and found to affect the chiral properties of a temporal SU(2) × SU(2) algebra. Finally, the symmetry between algebras is explored and pairs of algebras are found to be related by SU(2) × U(1) symmetry, while a group of three algebras are related by SO(4) symmetry.

APA, Harvard, Vancouver, ISO, and other styles

4

KERNER, RICHARD, and OSAMU SUZUKI. "INTERNAL SYMMETRY GROUPS OF CUBIC ALGEBRAS." International Journal of Geometric Methods in Modern Physics 09, no. 06 (August 3, 2012): 1261007. http://dx.doi.org/10.1142/s0219887812610075.

Full text

Abstract:

We investigate certain Z3-graded associative algebras with cubic Z3 invariant constitutive relations, introduced by one of us some time ago. The invariant forms on finite algebras of this type are given in the cases with two and three generators. We show how the Lorentz symmetry represented by the SL (2, C) group can be introduced without any notion of metric, just as the symmetry of Z3-graded cubic algebra and its constitutive relations. Its representation is found in terms of the Pauli matrices. The relationship of such algebraic constructions with quark states is also considered.

APA, Harvard, Vancouver, ISO, and other styles

5

Green, HS. "A Cyclic Symmetry Principle in Physics." Australian Journal of Physics 47, no. 1 (1994): 25. http://dx.doi.org/10.1071/ph940025.

Full text

Abstract:

Many areas of modern physics are illuminated by the application of a symmetry principle, requiring the invariance of the relevant laws of physics under a group of transformations. This paper examines the implications and some of the applications of the principle of cyclic symmetry, especially in the areas of statistical mechanics and quantum mechanics, including quantized field theory. This principle requires invariance under the transformations of a finite group, which may be a Sylow 7r-group, a group of Lie type, or a symmetric group. The utility of the principle of cyclic invariance is demonstrated in finding solutions of the Yang-Baxter equation that include and generalize known solutions. It is shown that the Sylow 7r-groups have other uses, in providing a basis for a type of generalized quantum statistics, and in parametrising a new generalization of Lie groups, with associated algebras that include quantized algebras.

APA, Harvard, Vancouver, ISO, and other styles

6

ĐAPIĆ, N., M. KUNZINGER, and S. PILIPOVIĆ. "SYMMETRY GROUP ANALYSIS OF WEAK SOLUTIONS." Proceedings of the London Mathematical Society 84, no. 3 (April 29, 2002): 686–710. http://dx.doi.org/10.1112/s0024611502013436.

Full text

Abstract:

Methods of Lie group analysis of differential equations are extended to weak solutions of (linear and non-linear) partial differential equations, where the term `weak solution' comprises the following settings: distributional solutions; solutions in generalized function algebras; solutions in the sense of association (corresponding to a number of weak or integral solution concepts in classical analysis). Factorization properties and infinitesimal criteria that allow the treatment of all three settings simultaneously are developed, thereby unifying and extending previous work in this area.2000 Mathematical Subject Classification: 46F30, 22E70, 35Dxx, 35A30.

APA, Harvard, Vancouver, ISO, and other styles

7

Elduque, Alberto, and Susumu Okubo. "Special Freudenthal–Kantor triple systems and Lie algebras with dicyclic symmetry." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 141, no. 6 (November 15, 2011): 1225–62. http://dx.doi.org/10.1017/s0308210510000569.

Full text

Abstract:

We study Lie algebras endowed with an action by automorphisms of the dicyclic group of degree 3. The close connections of these algebras with Lie algebras graded over the non-reduced root system BC1, with J-ternary algebras and with Freudenthal–Kantor triple systems are explored.

APA, Harvard, Vancouver, ISO, and other styles

8

Joardar, Soumalya, and Arnab Mandal. "Quantum symmetry of graph C∗-algebras associated with connected graphs." Infinite Dimensional Analysis, Quantum Probability and Related Topics 21, no. 03 (September 2018): 1850019. http://dx.doi.org/10.1142/s0219025718500194.

Full text

Abstract:

We define a notion of quantum automorphism groups of graph [Formula: see text]-algebras for finite, connected graphs. Under the assumption that the underlying graph does not have any multiple edge or loop, the quantum automorphism group of the underlying directed graph in the sense of Banica [Quantum automorphism groups of homogeneous graphs, J. Funct. Anal. 224 (2005) 243–280] (which is also the symmetry object in the sense of [S. Schmidt and M. Weber, Quantum symmetry of graph [Formula: see text]-algebras, arXiv:1706.08833 ] is shown to be a quantum subgroup of quantum automorphism group in our sense. Quantum symmetries for some concrete graph [Formula: see text]-algebras have been computed.

APA, Harvard, Vancouver, ISO, and other styles

9

Kamiya, Noriaki, and Susumu Okubo. "Symmetry of Lie algebras associated with (ε, δ)-Freudenthal-Kantor triple system." Proceedings of the Edinburgh Mathematical Society 59, no. 1 (July 13, 2015): 169–92. http://dx.doi.org/10.1017/s0013091514000406.

Full text

Abstract:

AbstractSymmetry groups of Lie algebras and superalgebras constructed from (∈, δ)-Freudenthal-Kantor triple systems have been studied. In particular, for a special (ε, ε)-Freudenthal–Kantor triple, it is the SL(2) group. Also, the relationship between two constructions of Lie algebras from structurable algebras has been investigated.

APA, Harvard, Vancouver, ISO, and other styles

10

DOLAN, L., and M. LANGHAM. "SYMMETRIC SUBGROUPS OF GAUGED SUPERGRAVITIES AND AdS STRING THEORY VERTEX OPERATORS." Modern Physics Letters A 14, no. 07 (March 7, 1999): 517–25. http://dx.doi.org/10.1142/s0217732399000572.

Full text

Abstract:

We show how the gauge symmetry representations of the massless particle content of gauged supergravities that arise in the AdS/CFT correspondences can be derived from symmetric subgroups to be carried by string theory vertex operators, although explicit vertex operator constructions of the IIB string on AdS remain elusive. Our symmetry mechanism parallels the construction of representations of the Monster group and affine algebras in terms of twisted conformal field theories, and may serve as a guide to a perturbative description of the IIB string on AdS.

APA, Harvard, Vancouver, ISO, and other styles

11

ALFINITO, ELEONORA, and GIUSEPPE VITIELLO. "TIME-REVERSAL, LOOP-ANTILOOP SYMMETRY AND THE BESSEL EQUATION." Modern Physics Letters B 17, no. 23 (October 10, 2003): 1207–18. http://dx.doi.org/10.1142/s0217984903006116.

Full text

Abstract:

The Bessel equation is shown to be equivalent, under suitable transformations, to a system of two damped/amplified parametric oscillator equations, which have been used in the study of inflationary models of the Universe, thermal field theories and Chern–Simons gauge theories. The breakdown of loop-antiloop symmetry due to group contraction manifests itself as breaking of time-reversal symmetry. The relation between some infinite dimensional loop-algebras, such as the Virasoro-like algebra, and the Euclidean algebras e(2) and e(3) is also analyzed.

APA, Harvard, Vancouver, ISO, and other styles

12

Lou, Sen-yue. "Symmetry Algebras and Group Invariant Solutions of the Kawamoto-Type Equations." Communications in Theoretical Physics 26, no. 3 (October 30, 1996): 311–18. http://dx.doi.org/10.1088/0253-6102/26/3/311.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

MATSUDA, SATOSHI, and YUKITAKA ISHIMOTO. "FEIGIN-FUKS REPRESENTATIONS FOR NONEQUIVALENT ALGEBRAS OF N=4 SUPERCONFORMAL SYMMETRY." Modern Physics Letters A 11, no. 32n33 (October 30, 1996): 2611–24. http://dx.doi.org/10.1142/s0217732396002617.

Full text

Abstract:

The N=4 SU (2)k superconformal algebra has the global automorphism of SO(4)≈ SU ((2)× SU ((2) with the left factor as the Kac-Moody gauge symmetry. As a consequence, an infinite set of independent algebras labeled by ρ corresponding to the conjugate classes of the outer automorphism group SO (4)/SU(2)= SU (2) are obtained à la Schwimmer and Seiberg. We construct Feigin-Fuks representations with the ρ parameter embedded for the infinite set of the N =4 nonequivalent algebras. In our construction the extended global SU(2) algebras labeled by ρ are self-consistently represented by fermion fields with appropriate boundary conditions.

APA, Harvard, Vancouver, ISO, and other styles

14

Kent, R. D., M. Schlesinger, and B. G. Wybourne. "Article." Canadian Journal of Physics 76, no. 6 (June 1, 1998): 445–52. http://dx.doi.org/10.1139/p98-032.

Full text

Abstract:

The role of Lie groups and algebras in symmetry-based models of the genetic code is considered. The two schemes, based upon the symplectic group Sp(6) and the exceptional group G(2) are shown to correspond to different embeddings in the group SO(14). Some possible alternative schemes are sketched. Problems with considering codons being represented as fermionic or bosonic are noted. A complete listing is given of all 64-dimensional irrecducible representations that can arise in the symmetric and alternating groups. PACS Nos.: 87.10 and 02.20

APA, Harvard, Vancouver, ISO, and other styles

15

Todorov, Ivan. "Gauge Symmetry and Howe Duality in 4D Conformal Field Theory Models." Advances in Mathematical Physics 2010 (2010): 1–12. http://dx.doi.org/10.1155/2010/509538.

Full text

Abstract:

It is known that there are no local scalar Lie fields in more than two dimensions. Bilocal fields, however, which naturally arise in conformal operator product expansions, do generate infinite Lie algebras. It is demonstrated that these Lie algebras of local observables admit (highly reducible) unitary positive energy representations in a Fock space. The multiplicity of their irreducible components is governed by a compact gauge group. The mutually commuting observable algebra and gauge group form a dual pair in the sense of Howe. In a theory of local scalar fields of conformal dimension two in four space-time dimensions the associated dual pairs are constructed and classified.

APA, Harvard, Vancouver, ISO, and other styles

16

de Wet, J. A. "Icosahedral Symmetry: A Review." International Frontier Science Letters 5 (October 2015): 1–8. http://dx.doi.org/10.18052/www.scipress.com/ifsl.5.1.

Full text

Abstract:

This Review covers over 40 years of research on using the algebras of Quarternions E6;E8to model Elementary Particle physics. In particular the Binary Icosahedral group is isomorphic to theExceptional Lie algebra E8 by the MacKay correspondence. And the toric graph of E8 in Fig.2 with240 vertices on 4 binary Riemann surfaces each carrying 60 vertices, models a solution of the Ernstequation for the stationary symmetric Einstein gravitational equation. Furthermore the 15 synthemesof E8, consisting of 5 sets of 3,can be identified with algebraic representations of the nucleon,supersymmetric particles,W bosons and Dark Matter.

APA, Harvard, Vancouver, ISO, and other styles

17

ABRAMOVICI, GILLES, and PAVEL KALUGIN. "CLIFFORD MODULES AND SYMMETRIES OF TOPOLOGICAL INSULATORS." International Journal of Geometric Methods in Modern Physics 09, no. 03 (May 2012): 1250023. http://dx.doi.org/10.1142/s0219887812500235.

Full text

Abstract:

We complete the classification of symmetry constraints on gapped quadratic fermion hamiltonians proposed by Kitaev. The symmetry group is supposed compact and can include arbitrary unitary or antiunitary operators in the Fock space that conserve the algebra of quadratic observables. We analyze the multiplicity spaces of real irreducible representations of unitary symmetries in the Nambu space. The joint action of intertwining operators and antiunitary symmetries provides these spaces with the structure of Clifford module: we prove a one-to-one correspondence between the ten Altland–Zirnbauer symmetry classes of fermion systems and the ten Morita equivalence classes of real and complex Clifford algebras. The antiunitary operators, which occur in seven classes, are projectively represented in the Nambu space by unitary "chiral symmetries". The space of gapped symmetric hamiltonians is homotopically equivalent to the product of classifying spaces indexed by the dual object of the group of unitary symmetries.

APA, Harvard, Vancouver, ISO, and other styles

18

Schmidt, Simon, and Moritz Weber. "Quantum Symmetries of Graph C*-algebras." Canadian Mathematical Bulletin 61, no. 4 (November 20, 2018): 848–64. http://dx.doi.org/10.4153/cmb-2017-075-4.

Full text

Abstract:

AbstractThe study of graph C*-algebras has a long history in operator algebras. Surprisingly, their quantum symmetries have not yet been computed. We close this gap by proving that the quantum automorphism group of a finite, directed graph without multiple edges acts maximally on the corresponding graph C*-algebra. This shows that the quantum symmetry of a graph coincides with the quantum symmetry of the graph C*-algebra. In our result, we use the definition of quantum automorphism groups of graphs as given by Banica in 2005. Note that Bichon gave a different definition in 2003; our action is inspired from his work. We review and compare these two definitions and we give a complete table of quantum automorphism groups (with respect to either of the two definitions) for undirected graphs on four vertices.

APA, Harvard, Vancouver, ISO, and other styles

19

Tam, Honwah, Yufeng Zhang, and Xiangzhi Zhang. "New Applications of a Kind of Infinitesimal-Operator Lie Algebra." Advances in Mathematical Physics 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/7639013.

Full text

Abstract:

Applying some reduced Lie algebras of Lie symmetry operators of a Lie transformation group, we obtain an invariant of a second-order differential equation which can be generated by a Euler-Lagrange formulism. A corresponding discrete equation approximating it is given as well. Finally, we make use of the Lie algebras to generate some new integrable systems including (1+1) and (2+1) dimensions.

APA, Harvard, Vancouver, ISO, and other styles

20

PAVLYUKH, YAROSLAV, and A. R. P. RAU. "1-, 2-, AND 6-QUBITS, AND THE RAMANUJAN–NAGELL THEOREM." International Journal of Quantum Information 11, no. 06 (September 2013): 1350056. http://dx.doi.org/10.1142/s0219749913500561.

Full text

Abstract:

A conjecture of Ramanujan that was later proved by Nagell is used to show on the basis of matching dimensions that only three n-qubit systems, for n = 1, 2, 6, can possibly share an isomorphism of their symmetry algebras with those of rotations in corresponding dimensions 3, 6, 91. Such isomorphisms are valuable for use in quantum information. Simple algebraic analysis, however, already rules out the last case so that one and two qubits are the only instances of such isomorphism of the algebras and of a local homomorphism of the corresponding symmetry groups. A more mathematical topological analysis of the group spaces is also provided demonstrating their topological inequivalence.

APA, Harvard, Vancouver, ISO, and other styles

21

Grundland, A. M., and L. Lalague. "Lie subgroups of the symmetry group of the equations describing a nonstationary and isentropic flow: Invariant and partially invariant solutions." Canadian Journal of Physics 72, no. 7-8 (July 1, 1994): 362–74. http://dx.doi.org/10.1139/p94-053.

Full text

Abstract:

We study the symmetries of the equations describing a nonstationary and isentropic flow for an ideal and compressible fluid in four-dimensional space-time. We prove that this system of equations is invariant under the Galilean-similitude group. In the special case of the adiabatic exponent γ = 5/3, corresponding to a diatomic gas, the symmetry group of this system is larger. It is invariant under the Galilean-projective group. A representatives list of subalgebras of Galilean similitude and Galilean-projective Lie algebras, obtained by the method of classification by conjugacy classes under the action of their respective Lie groups, is presented. The results are given in a normalized list and summarized in tables. Examples of invariant and nonreducible partially invariant solutions, obtained from this classification, is constructed. The final part of this work contains an analysis of this classification in connection with a further classification of the symmetry algebras for the Euler and magnetohydrodynamics equations.

APA, Harvard, Vancouver, ISO, and other styles

22

SZLACHÁNYI, K. "CHIRAL DECOMPOSITION AS A SOURCE OF QUANTUM SYMMETRY IN THE ISING MODEL." Reviews in Mathematical Physics 06, no. 04 (August 1994): 649–71. http://dx.doi.org/10.1142/s0129055x94000225.

Full text

Abstract:

The superselection sectors of three closely related models are studied and compared. I. The full Ising model with observable algebra [Formula: see text], the universal algebra of local even CAR algebras on the circle. [Formula: see text] has four sectors with Z(2) × Z(2) symmetry. II. The chiral Ising model with observable algebra [Formula: see text] (c = L or R), which is the universal algebra of local even Majorana algebras, has three sectors with quantum symmetry Gc ≅ M1⊕M1⊕M2. The Mack-Schomerus endomorphism creating the non-Abelian sector of [Formula: see text], respectively of [Formula: see text] is shown to coincide with the restriction [Formula: see text], respectively [Formula: see text] of a Z (2) charge creating automorphism ρ of [Formula: see text]. III. As an intermediate step the superselection sectors of the algebra [Formula: see text] — which can be interpreted as the observable algebra of the conformal Ising model — are found to have ordinary group symmetry described by the dihedral group D4. The relation between the sectors of [Formula: see text] and [Formula: see text] is explained in terms of a strange 'symmetry breaking': symmetry enhancement in the Neveu-Schwarz sector and symmetry breaking in the Ramond. Covariant charged fields are constructed in all three cases and the truncation in Gc is shown to arise from the failure of the Cuntz algebra relations for the chiral charged fields.

APA, Harvard, Vancouver, ISO, and other styles

23

BURDÍK, ČESTMÍR, A. PASHNEV, and M. TSULAIA. "ON THE MIXED SYMMETRY IRREDUCIBLE REPRESENTATIONS OF THE POINCARÉ GROUP IN THE BRST APPROACH." Modern Physics Letters A 16, no. 11 (April 10, 2001): 731–46. http://dx.doi.org/10.1142/s0217732301003826.

Full text

Abstract:

The Lagrangian description of irreducible massless representations of the Poincaré group with the corresponding Young tableaux having two rows along with some explicit examples including the notoph and Weyl tensor is given. For this purpose the method of the BRST constructions is adopted to the systems of second-class constraints by the construction of an auxiliary representations of the algebras of constraints in terms of Verma modules.

APA, Harvard, Vancouver, ISO, and other styles

24

GOVINDRAJAN, T. R., T. JAYRAMAN, AMITABH MUKHERJEE, and SPENTA R. WADIA. "TWISTED CURRENT ALGEBRAS AND GAUGE SYMMETRY BREAKING IN STRING THEORY." Modern Physics Letters A 01, no. 01 (April 1986): 29–36. http://dx.doi.org/10.1142/s0217732386000063.

Full text

Abstract:

The appearance of vorticity 01 twists in 2-dim. current algebra associated with a compact Lie group G can lead to the absence of some of the global symmetry generators of G and one expects the symmetry to be reduced to a smaller subgroup H of G. Contrary to expectations, all gauge bosons, including those of H become massive. This is because the zero point energy of the string is uniformly shifted upward affecting the masses of all particles by the same amount.

APA, Harvard, Vancouver, ISO, and other styles

25

Bai, Ruipu, Lixin Lin, Yan Zhang, and Chuangchuang Kang. "q-Deformations of 3-Lie Algebras." Algebra Colloquium 24, no. 03 (September 2017): 519–40. http://dx.doi.org/10.1142/s1005386717000347.

Full text

Abstract:

q-Deformations of 3-Lie algebras and representations of q-3-Lie algebras are discussed. A q-3-Lie algebra [Formula: see text], where [Formula: see text] and [Formula: see text], is a vector space A over a field 𝔽 with 3-ary linear multiplications [ , , ]q and [Formula: see text] from [Formula: see text] to A, and a map [Formula: see text] satisfying the q-Jacobi identity [Formula: see text] for all [Formula: see text]. If the multiplications satisfy that [Formula: see text] and [Formula: see text] is skew-symmetry, then [Formula: see text] is called a type (I)-q-3- Lie algebra. From q-Lie algebras, group algebras and commutative associative algebras, q-3-Lie algebras and type (I)-q-3-Lie algebras are constructed. Also, the non-trivial onedimensional central extension of q-3-Lie algebras is investigated, and new q-3-Lie algebras [Formula: see text], and [Formula: see text] are obtained.

APA, Harvard, Vancouver, ISO, and other styles

26

ABDALLA, E., M. C. B. ABDALLA, G. SOTKOV, and M. STANISHKOV. "OFF-CRITICAL CURRENT ALGEBRAS." International Journal of Modern Physics A 10, no. 12 (May 10, 1995): 1717–36. http://dx.doi.org/10.1142/s0217751x95000838.

Full text

Abstract:

We discuss the infinite-dimensional algebras appearing in integrable perturbations of conformally invariant theories, with special emphasis on the structure of the consequent non-Abelian infinite-dimensional algebra generalizing W∞ to the case of a non-Abelian group. We prove that the pure left sector as well as the pure right sector of the thus-obtained algebra coincides with the conformally invariant case. The mixed sector is more involved, although the general structure seems to be near to being unraveled. We also find some subalgebras that correspond to Kac-Moody algebras. The constraints imposed by the algebras are very strong and, in the case of the massive deformation of a non-Abelian fermionic model, the symmetry alone is enough to fix the two- and three-point functions of the theory.

APA, Harvard, Vancouver, ISO, and other styles

27

Khorshidi, Maryam, Mehdi Nadjafikhah, Hossein Jafari, and Maysaa Al Qurashi. "Reductions and conservation laws for BBM and modified BBM equations." Open Mathematics 14, no. 1 (January 1, 2016): 1138–48. http://dx.doi.org/10.1515/math-2016-0101.

Full text

Abstract:

AbstractIn this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM) and modified Benjamin-Bona-Mahony equations (MBBM) to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system) of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations. Finally, conservation laws of the BBM and MBBM equations are presented. Some aspects of their symmetry properties are given too.

APA, Harvard, Vancouver, ISO, and other styles

28

Simulik, V. M., and I. O. Gordievich. "Symmetries of Relativistic Hydrogen Atom." Ukrainian Journal of Physics 64, no. 12 (December 9, 2019): 1148. http://dx.doi.org/10.15407/ujpe64.12.1148.

Full text

Abstract:

The Dirac equation in the external Coulomb field is proved to possess the symmetry determined by 31 operators, which form the 31-dimensional algebra. Two different fermionic realizations of the SO(1,3) algebra of the Lorentz group are found. Two different bosonic realizations of this algebra are found as well. All generators of the above-mentioned algebras commute with the operator of the Dirac equation in an external Coulomb field and, therefore, determine the algebras of invariance of such Dirac equation. Hence, the spin s = (1, 0) Bose symmetry of the Dirac equation for the free spinor field, proved recently in our papers, is extended here for the Dirac equation interacting with an external Coulomb field. A relativistic hydrogen atom is modeled by such Dirac equation. We are able to prove for the relativistic hydrogen atom both the fermionic and bosonic symmetries known from our papers in the case of a non-interacting spinor field. New symmetry operators are found on the basis of new gamma matrix representations of the Clifford and SO(8) algebras, which are known from our recent papers as well. Hidden symmetries were found both in the canonical Foldy–Wouthuysen and covariant Dirac representations. The found symmetry operators, which are pure matrix ones in the Foldy–Wouthuysen representation, become non-local in the Dirac model.

APA, Harvard, Vancouver, ISO, and other styles

29

Bolokhov, S. V., and V. D. Ivashchuk. "Duality Identities for Moduli Functions of Generalized Melvin Solutions Related to Classical Lie Algebras of Rank 4." Advances in Mathematical Physics 2018 (November 7, 2018): 1–10. http://dx.doi.org/10.1155/2018/8179570.

Full text

Abstract:

We consider generalized Melvin-like solutions associated with nonexceptional Lie algebras of rank 4 (namely, A4, B4, C4, and D4) corresponding to certain internal symmetries of the solutions. The system under consideration is a static cylindrically symmetric gravitational configuration in D dimensions in presence of four Abelian 2-forms and four scalar fields. The solution is governed by four moduli functions Hs(z) (s=1,…,4) of squared radial coordinate z=ρ2 obeying four differential equations of the Toda chain type. These functions turn out to be polynomials of powers (n1,n2,n3,n4)=(4,6,6,4),(8,14,18,10),(7,12,15,16),(6,10,6,6) for Lie algebras A4, B4, C4, and D4, respectively. The asymptotic behaviour for the polynomials at large distances is governed by some integer-valued 4×4 matrix ν connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in A4 case) the matrix representing a generator of the Z2-group of symmetry of the Dynkin diagram. The symmetry properties and duality identities for polynomials are obtained, as well as asymptotic relations for solutions at large distances. We also calculate 2-form flux integrals over 2-dimensional discs and corresponding Wilson loop factors over their boundaries.

APA, Harvard, Vancouver, ISO, and other styles

30

Reid, Gregory J. "Finding abstract Lie symmetry algebras of differential equations without integrating determining equations." European Journal of Applied Mathematics 2, no. 4 (December 1991): 319–40. http://dx.doi.org/10.1017/s0956792500000589.

Full text

Abstract:

There are symbolic programs based on heuristics that sometimes, but not always, explicitly integrate the determining equations for the infinitesimal Lie symmetries admitted by systems of differential equations. We present a heuristic-free algorithm ‘Structure constant’, which can always determine whether the Lie symmetry group of a given system of PDEs is finite- or infinite-dimensional. If the group is finite-dimensional then ‘Structure constant’ can determine the dimension and structure constants of its associated Lie algebra without the heuristics of integration involved in other methods. If the group is infinite-dimensional, then ‘Structure constant’ computes the number of arbitrary functions which determine the infinite-dimensional component of its Lie symmetry algebra and also calculates the dimension and structure of its associated finite-dimensional subalgebra. ‘Structure constant’ employs the algorithms ‘Standard form’ and ‘Taylor’, described elsewhere. ‘Standard form’ is a heuristic-free algorithm which brings any system of determining equations to a standard form by including all integrability conditions in the system. ‘Taylor’ uses the standard form of a system of differential equations to calculate its Taylor series solution. These algorithms have been implemented in the symbolic language MAPLE. ‘Structure constant’ can also automatically determine the dimension and structure constants of the Lie symmetry algebras of entire classes of differential equations dependent on variable coefficients. In particular, we obtain new group classification results for some physically interesting classes of nonlinear telegraph equations depending on two variable coefficients, one representing a nonlinear wave speed and the other representing a nonlinear dispersion.

APA, Harvard, Vancouver, ISO, and other styles

31

Cortés, V., L. Gall, and T. Mohaupt. "Four-dimensional vector multiplets in arbitrary signature (I)." International Journal of Geometric Methods in Modern Physics 17, no. 10 (August 26, 2020): 2050150. http://dx.doi.org/10.1142/s0219887820501509.

Full text

Abstract:

We derive a necessary and sufficient condition for Poincaré Lie superalgebras in any dimension and signature to be isomorphic. This reduces the classification problem, up to certain discrete operations, to classifying the orbits of the Schur group on the vector space of superbrackets. We then classify four-dimensional [Formula: see text] supersymmetry algebras, which are found to be unique in Euclidean and in neutral signature, while in Lorentz signature there exist two algebras with R-symmetry groups [Formula: see text] and [Formula: see text], respectively.

APA, Harvard, Vancouver, ISO, and other styles

32

BELLON, M., J.-M. MAILLARD, and C. VIALLET. "ON THE SYMMETRIES OF INTEGRABILITY." International Journal of Modern Physics B 06, no. 11n12 (June 1992): 1881–903. http://dx.doi.org/10.1142/s021797929200092x.

Full text

Abstract:

We show that the Yang-Baxter equations for two-dimensional models admit as a group of symmetry the infinite discrete group [Formula: see text]. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. We show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. We indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiate the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non-trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. We mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. Our results also yield the generalization of the condition qn=1 so often mentioned in the theory of quantum groups, when no q parameter is available.

APA, Harvard, Vancouver, ISO, and other styles

33

FREDENHAGEN, KLAUS, KARL-HENNING REHREN, and BERT SCHROER. "SUPERSELECTION SECTORS WITH BRAID GROUP STATISTICS AND EXCHANGE ALGEBRAS II: GEOMETRIC ASPECTS AND CONFORMAL COVARIANCE." Reviews in Mathematical Physics 04, spec01 (December 1992): 113–57. http://dx.doi.org/10.1142/s0129055x92000170.

Full text

Abstract:

The general theory of superselection sectors is shown to provide almost all the structure observed in two-dimensional conformal field theories. Its application to two-dimensional conformally covariant and three-dimensional Poincaré covariant theories yields a general spin-statistics connection previously encountered in more special situations. CPT symmetry can be shown also in the absence of local (anti-) commutation relations, if the braid group statistics is expressed in the form of an exchange algebra.

APA, Harvard, Vancouver, ISO, and other styles

34

Wolk, Brian Jonathan. "The underlying geometry of the CAM gauge model of the Standard Model of particle physics." International Journal of Modern Physics A 35, no. 07 (March 10, 2020): 2050037. http://dx.doi.org/10.1142/s0217751x20500372.

Full text

Abstract:

The Composition Algebra-based Methodology (CAM) [B. Wolk, Pap. Phys. 9, 090002 (2017); Phys. Scr. 94, 025301 (2019); Adv. Appl. Clifford Algebras 27, 3225 (2017); J. Appl. Math. Phys. 6, 1537 (2018); Phys. Scr. 94, 105301 (2019), Adv. Appl. Clifford Algebras 30, 4 (2020)], which provides a new model for generating the interactions of the Standard Model, is geometrically modeled for the electromagnetic and weak interactions on the parallelizable sphere operator fiber bundle [Formula: see text] consisting of base space, the tangent bundle [Formula: see text] of space–time [Formula: see text], projection operator [Formula: see text], the parallelizable spheres [Formula: see text] conceived as operator fibers [Formula: see text] attaching to and operating on [Formula: see text] [Formula: see text] as [Formula: see text] varies over [Formula: see text], and as structure group, the norm-preserving symmetry group [Formula: see text] for each of the division algebras which is simultaneously the isometry group of the associated unit sphere. The massless electroweak [Formula: see text] Lagrangian is shown to arise from [Formula: see text]’s generation of a local coupling operation on sections of Dirac spinor and Clifford algebra bundles over [Formula: see text]. Importantly, CAM is shown to be a new genre of gauge theory which subsumes Yang–Mills Standard Model gauge theory. Local gauge symmetry is shown to be at its core a geometric phenomenon inherent to CAM gauge theory. Lastly, the higher-dimensional, topological architecture which generates CAM from within a unified eleven [Formula: see text]-dimensional geometro-topological structure is introduced.

APA, Harvard, Vancouver, ISO, and other styles

35

Janda, Jiří. "Weakly ordered partial commutative group of self-adjoint linear operators densely defined on Hilbert space." Tatra Mountains Mathematical Publications 50, no. 1 (December 1, 2011): 63–78. http://dx.doi.org/10.2478/v10127-011-0037-x.

Full text

Abstract:

ABSTRACT We continue in a direction of describing an algebraic structure of linear operators on infinite-dimensional complex Hilbert space ℋ. In [Paseka, J.- -Janda, J.: More on PT-symmetry in (generalized) effect algebras and partial groups, Acta Polytech. 51 (2011), 65-72] there is introduced the notion of a weakly ordered partial commutative group and showed that linear operators on H with restricted addition possess this structure. In our work, we are investigating the set of self-adjoint linear operators on H showing that with more restricted addition it also has the structure of a weakly ordered partial commutative group.

APA, Harvard, Vancouver, ISO, and other styles

36

GERASIMOV, A., YU MAKEENKO, A. MARSHAKOV, A. MIRONOV, A. MOROZOV, and A. ORLOV. "MATRIX MODELS AS INTEGRABLE SYSTEMS: FROM UNIVERSALITY TO GEOMETRODYNAMICAL PRINCIPLE OF STRING THEORY." Modern Physics Letters A 06, no. 33 (October 30, 1991): 3079–90. http://dx.doi.org/10.1142/s0217732391003572.

Full text

Abstract:

Matrix models are equivalent to certain integrable theories, partition functions being equal to certain τ-functions, i.e., the section of determinant bundles over infinite-dimensional Grassmannian. These τ-functions are evaluated at the points of Grassmannian, where high symmetry arises. In the case of one-matrix models the symmetry is isomorphic to Borel subgroup of a Virasoro group. The orbits of the group are in one-to-one correspondence with the types of "multicritical" behavior in the continuum limit. Interrelation between τ-functions in different models and their continuum limit is discussed in some details. We also discuss the implications for dynamical interpolation between various string models (CFT's), to be described in terms of geometrical quantization of Fairlie-like [Formula: see text]-algebras.

APA, Harvard, Vancouver, ISO, and other styles

37

CHAO, LIU, and BO-YU HOU. "BOSONIC SUPERCONFORMAL AFFINE TODA THEORY: EXCHANGE ALGEBRA AND DRESSING SYMMETRY." International Journal of Modern Physics A 08, no. 21 (August 20, 1993): 3773–89. http://dx.doi.org/10.1142/s0217751x93001533.

Full text

Abstract:

We propose and investigate a new conformal invariant integrable field theory called bosonic superconformal affine Toda theory. This theory can be viewed either as the affine generalization of the so-called bosonic superconformal Toda theory studied by the authors sometime earlier, or as the generalization to the case of half-integer conformal weights of the conformal affine Toda theory, and can also be obtained from the Hamiltonian reduction of WZNW theory (with an affine WZNW group). The fundamental Poisson stracture is established in terms of the classical r matrix. Then the exchange algebra for the chiral vectors is obtained as well as the reconstruction formula for the classical solutions. The dressing transformations of the fundamental fields are found explicitly, and the Poisson-Lie structure of the dressing group is also constructed with the aid of classical exchange algebras, which turns out to be the semiclassical limit of the quantum affine group. The conformal breaking orbit of the model is also studied, which is called bosonic super loop Toda theory in the context. In addition, the quantum exchange relation and quantum group symmetry are discussed briefly.

APA, Harvard, Vancouver, ISO, and other styles

38

GABERDIEL, MATTHIAS. "FUSION IN CONFORMAL FIELD THEORY AS THE TENSOR PRODUCT OF THE SYMMETRY ALGEBRA." International Journal of Modern Physics A 09, no. 26 (October 20, 1994): 4619–36. http://dx.doi.org/10.1142/s0217751x94001849.

Full text

Abstract:

Following a recent proposal of Richard Borcherds to regard fusion as the ringlike tensor product of modules of a quantum ring, a generalization of rings and vertex algebras, we define fusion as a certain quotient of the (vector space) tensor product of representations of the symmetry algebra [Formula: see text]. We prove that this tensor product is associative and symmetric up to equivalence. We also determine explicitly the action of [Formula: see text] on it, under which the central extension is preserved. Having defined fusion in this way, determining the fusion rules is then the algebraic problem of decomposing the tensor product into irreducible representations. We demonstrate how to solve this for the case of the WZW and the minimal models and recover thereby the well-known fusion rules. The action of the symmetry algebra on the tensor product is given in terms of a comultiplication. We calculate the R matrix of this comultiplication and find that it is triangular. This seems to shed some new light on the possible rôle of the quantum group in conformal field theory.

APA, Harvard, Vancouver, ISO, and other styles

39

Petitjean, Michel. "Chirality of Dirac Spinors Revisited." Symmetry 12, no. 4 (April 14, 2020): 616. http://dx.doi.org/10.3390/sym12040616.

Full text

Abstract:

We emphasize the differences between the chirality concept applied to relativistic fermions and the ususal chirality concept in Euclidean spaces. We introduce the gamma groups and we use them to classify as direct or indirect the symmetry operators encountered in the context of Dirac algebra. Then we show how a recent general mathematical definition of chirality unifies the chirality concepts and resolve conflicting conclusions about symmetry operators, and particularly about the so-called chirality operator. The proofs are based on group theory rather than on Clifford algebras. The results are independent on the representations of Dirac gamma matrices, and stand for higher dimensional ones.

APA, Harvard, Vancouver, ISO, and other styles

40

ABBASPUR, REZA. "GENERALIZED NONCOMMUTATIVE SUPERALGEBRAS." Modern Physics Letters A 18, no. 08 (March 14, 2003): 587–99. http://dx.doi.org/10.1142/s0217732303009551.

Full text

Abstract:

Using the notions of gauge symmetry and gauge connection on ordinary superspaces, we derive a class of generalized supertranslation algebras in the case of N = 1, D = 2 Euclidean superspace with a U(1) gauge group. This generalizes the ordinary algebra by inclusion of some additional bosonic and fermionic operators which are interpreted as the generators of the U(1) gauge symmetry on superspace. The generalized superalgebra closes only for very particular configurations of the gauge connection superfield. This provides a unified framework for a variety of generalizations of the ordinary superalgebra such as its central extension and its noncommutative deformation found in an earlier work.

APA, Harvard, Vancouver, ISO, and other styles

41

HOLLANDS, STEFAN. "ALGEBRAIC APPROACH TO THE 1/N EXPANSION IN QUANTUM FIELD THEORY." Reviews in Mathematical Physics 16, no. 04 (May 2004): 509–58. http://dx.doi.org/10.1142/s0129055x04002072.

Full text

Abstract:

The 1/N expansion in quantum field theory is formulated within an algebraic framework. For a scalar field taking values in the N by N hermitian matrices, we rigorously construct the gauge invariant interacting quantum field operators in the sense of power series in 1/N and the 't Hooft coupling parameter as members of an abstract *-algebra. The key advantages of our algebraic formulation over the usual formulation of the 1/N expansion in terms of Green's functions are (i) that it is completely local so that infrared divergencies in massless theories are avoided on the algebraic level and (ii) that it admits a generalization to quantum field theories on globally hypberbolic Lorentzian curved spacetimes. We expect that our constructions are also applicable in models possessing local gauge invariance such as Yang–Mills theories. The 1/N expansion of the renormalization group flow is constructed on the algebraic level via a family of *-isomorphisms between the algebras of interacting field observables corresponding to different scales. We also consider k-parameter deformations of the interacting field algebras that arise from reducing the symmetry group of the model to a diagonal subgroup with k factors. These parameters smoothly interpolate between situations of different symmetry.

APA, Harvard, Vancouver, ISO, and other styles

42

KUNDU, A., and B. BASU MALLICK. "CONSTRUCTION OF INTEGRABLE QUANTUM LATTICE MODELS THROUGH SKLYANIN-LIKE ALGEBRAS." Modern Physics Letters A 07, no. 01 (January 10, 1992): 61–69. http://dx.doi.org/10.1142/s0217732392003438.

Full text

Abstract:

A systematic approach for generation of integrable quantum lattice models exploiting the underlying Uq(2) quantum group structure as well as its multiparameter generalization is presented. We find an extension of trigonometric Sklyanin algebra and also its deformation through "symmetry breaking transformation," which after consistent bosonization (or q-bosonization) construct a series of integrable lattice models. A novel quantum solvable derivative NLS, a relativistic Toda chain and a lattice model involving q-oscillators warrant special mention. As an added advantage, along with the integrable models the corresponding quantum R-matrices are also specified.

APA, Harvard, Vancouver, ISO, and other styles

43

PERCACCI, R., and E. SEZGIN. "SYMMETRIES OF p-BRANES." International Journal of Modern Physics A 08, no. 30 (December 10, 1993): 5367–81. http://dx.doi.org/10.1142/s0217751x93002137.

Full text

Abstract:

Using canonical methods, we study the invariance properties of a bosonic p-brane propagating in a curved background locally diffeomorphic to M×G, where M is space-time and G a group manifold. The action is that of a gauged sigma model in p+1 dimensions coupled to a Yang-Mills field and a (p+1) form in M. We construct the generators of Yang-Mills and tensor gauge transformations and exhibit the role of the (p+1) form in canceling the potential Schwinger terms. We also discuss the Noether currents associated with the global symmetries of the action and the question of the existence of infinite-dimensional symmetry algebras, analogous to the Kac-Moody symmetry of the string.

APA, Harvard, Vancouver, ISO, and other styles

44

Vilela Mendes, R. "Space–times over normed division algebras, revisited." International Journal of Modern Physics A 35, no. 10 (April 10, 2020): 2050055. http://dx.doi.org/10.1142/s0217751x20500554.

Full text

Abstract:

Normed division and Clifford algebras have been extensively used in the past as a mathematical framework to accommodate the structures of the Standard Model and grand unified theories. Less discussed has been the question of why such algebraic structures appear in Nature. One possibility could be an intrinsic complex, quaternionic or octonionic nature of the space–time manifold. Then, an obvious question is why space–time appears nevertheless to be simply parametrized by the real numbers. How the real slices of an higher-dimensional space–time manifold might be almost independent from each other is discussed here. This comes about as a result of the different nature of the representations of the real kinematical groups and those of the extended spaces. Some of the internal symmetry transformations might however appear as representations on homogeneous spaces of the extended group transformations that cannot be implemented on the elementary states.

APA, Harvard, Vancouver, ISO, and other styles

45

DENG, YUEFAN, ALEXANDRE F. RAMOS, and JOSÉ EDUARDO M. HORNOS. "SYMMETRY INSIGHTS FOR DESIGN OF SUPERCOMPUTER NETWORK TOPOLOGIES: ROOTS AND WEIGHTS LATTICES." International Journal of Modern Physics B 26, no. 31 (December 4, 2012): 1250169. http://dx.doi.org/10.1142/s021797921250169x.

Full text

Abstract:

We present a family of networks whose local interconnection topologies are generated by the root vectors of a semi-simple complex Lie algebra. Cartan classification theorem of those algebras ensures those families of interconnection topologies to be exhaustive. The global arrangement of the network is defined in terms of integer or half-integer weight lattices. The mesh or torus topologies that network millions of processing cores, such as those in the IBM BlueGene series, are the simplest member of that category. The symmetries of the root systems of an algebra, manifested by their Weyl group, lends great convenience for the design and analysis of hardware architecture, algorithms and programs.

APA, Harvard, Vancouver, ISO, and other styles

46

JORGENSEN, PALLE E. T. "REPRESENTATIONS OF LIE ALGEBRAS BUILT OVER HILBERT SPACE." Infinite Dimensional Analysis, Quantum Probability and Related Topics 14, no. 03 (September 2011): 419–42. http://dx.doi.org/10.1142/s0219025711004468.

Full text

Abstract:

Starting with a complex Hilbert space, using inductive limits, we build Lie algebras, and find families of representations. They include those often studied in mathematical physics in order to model quantum statistical mechanics or quantum fields. We explore natural actions on infinite tensor algebras T(H) built with a functorial construction, starting with a fixed Hilbert space H. While our construction applies also when H is infinite-dimensional, the case with N ≔ dim H finite is of special interest as the symmetry group we consider is then a copy of the non-compact Lie group U(N, 1). We give the tensor algebra T(H) the structure of a Hilbert space, i.e. the unrestricted infinite tensor product Fock space [Formula: see text]. The tensor algebra T(H) is naturally represented as acting by bounded operators on [Formula: see text], and U (N, 1) as acting as a unitary representation. From this we built a covariant system, and we explore how the fermion, the boson, and the q on Hilbert spaces are reduced by the representations. In particular we display the decomposition into irreducible representations of the naturally defined U (N, 1) representation.

APA, Harvard, Vancouver, ISO, and other styles

47

Haapasalo, Erkka, and Juha-Pekka Pellonpää. "Covariant KSGNS construction and quantum instruments." Reviews in Mathematical Physics 29, no. 07 (August 2017): 1750020. http://dx.doi.org/10.1142/s0129055x17500209.

Full text

Abstract:

We study completely positive (CP) [Formula: see text]-sesquilinear-form-valued maps on a unital [Formula: see text]-algebra [Formula: see text], where the sesquilinear forms operate on a module over a [Formula: see text]-algebra [Formula: see text]. We also study the cases when either one or both of the algebras are von Neumann algebras. Moreover, we assume that the CP maps are covariant with respect to actions of a symmetry group. This allows us to view these maps as generalizations of covariant quantum instruments. We determine minimal covariant dilations (KSGNS constructions) for covariant CP maps to find necessary and sufficient conditions for a CP map to be extreme in convex subsets of normalized covariant CP maps. As a special case, we study covariant quantum observables and instruments whose value space is a transitive space of a unimodular type-I group. Finally, we discuss the case of instruments that are covariant with respect to a square-integrable representation.

APA, Harvard, Vancouver, ISO, and other styles

48

MASLIKOV, A. A., S. M. SERGEEV, and G. G. VOLKOV. "STRING-MOTIVATED GRAND UNIFIED THEORIES WITH HORIZONTAL GAUGE SYMMETRY." International Journal of Modern Physics A 09, no. 30 (December 10, 1994): 5369–85. http://dx.doi.org/10.1142/s0217751x94002156.

Full text

Abstract:

In the framework of four-dimensional heterotic superstring with free fermions, we investigate the rank 8 grand unified string theories (GUST’s) which contain the SU(3) H gauge family symmetry. GUST’s of this type accommodate naturally the three fermion families presently observed and, moreover, can describe the fermion mass spectrum without high-dimensional representations of conventional unification groups. We explicitly construct GUST’s with gauge symmetry G= SU(5) × U(1) ×[ SU(3) × U(1) ]H ⊂ SO (16) in free complex fermion formulation. As the GUST’s originating from Kac-Moody algebras (KMA’s) contain only low-dimensional representations, it is usually difficult to break the gauge symmetry. We solve this problem by taking for the observable gauge symmetry the diagonal subgroup G sym of the rank 16 group G×G ⊂ SO(16) × SO(16) ⊂ E(8)×E(8). Such a construction effectively corresponds to a level 2 KMA, and therefore some higher-dimensional representations of the diagonal subgroup appear. This (due to G×G tensor Higgs fields) allows one to break GUST symmetry down to SU (3c)× U(1) em . In this approach the observed electromagnetic charge Q em can be viewed as a sum of two Q I and Q II charges of each G group. In this case, below the scale where G×G breaks down to G sym the spectrum does not contain particles with exotic fractional charges.

APA, Harvard, Vancouver, ISO, and other styles

49

Maslikov, Alexander, and Guennady Volkov. "Ternary SU(3)-group symmetry and its possible applications in hadron-quark substructure. Towards a new spinor-fermion structure." EPJ Web of Conferences 204 (2019): 02007. http://dx.doi.org/10.1051/epjconf/201920402007.

Full text

Abstract:

The questions on the existence of the three color quark symmetry and three quark-lepton generations could have the origin associated with the new exotic symmetries outside the Cartan-Killing-Lie algebras/groups. Our long-term search for these symmetries has been began with our Calabi-Yau space classification on the basis of the n-ary algebra for the reflexive projective numbers and led us to the expansion of the binary n = 2 complex and hyper complex numbers in the framework of the n-ary complex and hyper-complex numbers with n = 3, 4, … where we constructed new Abelian and non-Abelian symmetries. We have studied then norm-division properties of the Abelian nary complex numbers and have built the infinite chain of the Abelian groups U(n–1) = [U(1) × … × U(1)](n–1). We have developed the n-ary holomorphic (polymorphic) analysis on the n-ary complex space NC{n}, which led us to the generalization of the quadratic Laplace equations for the harmonic functions. The generalized Laplace equations for the n-ary harmonic functions give us the n-th order homogeneous differential equations which are invariant with respect to the Abelian n-ary groups U(n–1) and with some new spatial properties. Further consideration of the non-Abelian n-ary hyper-complex numbers opens the infinite series of the non-Abelian TnSU(n)-Lie groups(n=3,4,…) and its corresponding tnsu(n) algebras. One of the exceptional features of these symmetry groups is the appearance of some new n-dimensional spinors that could lead to an extension of the concept of the SU(2)-spin, to the appearance of n-dimensional quantum structures -exotic “n-spinor” matter(n = 3, 4, … - maarcrions). It is natural to assume that these new exotic “quantum spinor states” could be candidates for the pra-matter of the quark-charge leptons or/and for the dark matter. We will be also interested in the detection of the exotic quantum ’n-spinor” matter in the neutrino and hadron experiments.

APA, Harvard, Vancouver, ISO, and other styles

50

Shvedov, Oleg Yu. "Symmetries of semiclassical gauge systems." International Journal of Geometric Methods in Modern Physics 12, no. 10 (October 25, 2015): 1550110. http://dx.doi.org/10.1142/s0219887815501108.

Full text

Abstract:

Semiclassical systems being symmetric under Lie group are studied. A state of a semiclassical system may be viewed as a set (X, f) of a classical state X and a quantum state f in the external classical background X. Therefore, the set of all semiclassical states may be considered as a bundle (semiclassical bundle). Its base {X} is the set of all classical states, while a fiber is a Hilbert space ℱX of quantum states in the external background X. Symmetry transformation of a semiclassical system may be viewed as an automorphism of the semiclassical bundle. Automorphism groups can be investigated with the help of sections of the bundle: to any automorphism of the bundle one assigns a transformation of section of the bundle. Infinitesimal properties of transformations of sections are investigated; correspondence between Lie groups and Lie algebras is discussed. For gauge theories, some points of the semiclassical bundle are identified: a gauge group acts on the bundle. For this case, only gauge-invariant sections of the semiclassical bundle are taken into account.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!