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Journal articles on the topic 'Weyle invariance'

Author: Grafiati

Published: 14 March 2023

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1

NIETO, J. A. "REMARKS ON WEYL INVARIANT p-BRANES AND Dp-BRANES." Modern Physics Letters A 16, no. 40 (December 28, 2001): 2567–78. http://dx.doi.org/10.1142/s0217732301005497.

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A mechanism to find different Weyl invariant p-branes and Dp-branes actions is explained. Our procedure clarifies the Weyl invariance for such systems. Besides, by considering gravity–dilaton effective action in higher dimensions, we also derive a Weyl invariant action for p-branes. We argue that this derivation provides a geometrical scenario for the Weyl invariance of p-branes. Our considerations can be extended to the case of super-p-branes.

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2

Edery, Ariel, and Yu Nakayama. "Generating Einstein gravity, cosmological constant and Higgs mass from restricted Weyl invariance." Modern Physics Letters A 30, no. 30 (September 7, 2015): 1550152. http://dx.doi.org/10.1142/s0217732315501527.

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Recently, it has been pointed out that dimensionless actions in four-dimensional curved spacetime possess a symmetry which goes beyond scale invariance but is smaller than full Weyl invariance. This symmetry was dubbed restricted Weyl invariance. We show that starting with a restricted Weyl invariant action that includes a Higgs sector with no explicit mass, one can generate the Einstein–Hilbert action with cosmological constant and a Higgs mass. The model also contains an extra massless scalar field which couples to the Higgs field (and gravity). If the coupling of this extra scalar field to the Higgs field is negligibly small, this fixes the coefficient of the nonminimal coupling [Formula: see text] between the Higgs field and gravity. Besides the Higgs sector, all the other fields of the Standard Model can be incorporated into the original restricted Weyl invariant action.

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3

Futorny, Vyacheslav, and João Schwarz. "Holonomic modules for rings of invariant differential operators." International Journal of Algebra and Computation 31, no. 04 (April 10, 2021): 605–22. http://dx.doi.org/10.1142/s0218196721500296.

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We study holonomic modules for the rings of invariant differential operators on affine commutative domains with finite Krull dimension with respect to arbitrary actions of finite groups. We prove the Bernstein inequality for these rings. Our main tool is the filter dimension introduced by Bavula. We extend the results for the invariants of the Weyl algebra with respect to the symplectic action of a finite group, for the rings of invariant differential operators on quotient varieties, and invariants of certain generalized Weyl algebras under the linear actions. We show that the filter dimension of all above mentioned algebras equals 1.

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4

SUZUKI, HIROSHI. "THERMAL PARTITION FUNCTION OF NON-CRITICAL BOSONIC STRINGS." Modern Physics Letters A 04, no. 21 (October 20, 1989): 2085–92. http://dx.doi.org/10.1142/s0217732389002343.

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The thermal free energy of free non-critical bosonic strings in a D-dimensional spacetime is examined. By integrating (or summing) over the Weyl freedom, the free energy and the one-loop vacuum amplitude are modular invariant for any D<26. Thus the (background) Weyl invariance is realized. In the case of L→∞, where L is the compactification radius of the Weyl mode, the physical spectrum circulating in the loop becomes continuous. A connection between this continuous spectrum and the unitarity of string perturbation theory is briefly mentioned.

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5

JAIN, SANJAY. "CONFORMALLY INVARIANT FIELD THEORY IN TWO DIMENSIONS AND STRINGS IN CURVED SPACETIME." International Journal of Modern Physics A 03, no. 08 (August 1988): 1759–846. http://dx.doi.org/10.1142/s0217751x8800076x.

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The formalism of conformally invariant field theory on a 2-dimensional real manifold with an intrinsic metric is developed in the functional integral framework. This formalism is used to study the relationships between reparametrization, Weyl, conformal and BRST invariances for strings in generic backgrounds. Conformal invariance of string amplitudes in the presence of backgrounds is formulated in terms of the Virasoro conditions, i.e., that physical vertex operators generate (1,1) representations of the Virasoro algebra, or, equivalently, the condition Q|Ψ〉=0 on physical states |Ψ〉, where Q is the BRST charge. The consequences of these conditions are investigated in the case of specific backgrounds. Strings in group manifolds are discussed exactly. For a generic slowly varying spacetime metric and dilaton field, a perturbatively renormalized vertex operator solution to the Virasoro conditions is constructed. It is shown that the existence of a solution to the Virasoro conditions or the equation Q|Ψ〉=0 requires the spacetime metric to satisfy Einstein’s equations. These conditions therefore constitute equations of motion for both the spectrum and backgrounds of string theory.

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6

CHO, Y. M. "MONOPOLE CONDENSATION AND MASS GAP IN SU(3) QCD." International Journal of Modern Physics A 29, no. 03n04 (February 10, 2014): 1450013. http://dx.doi.org/10.1142/s0217751x14500134.

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We demonstrate the monopole condensation in SU(3) QCD. We first discuss the gauge independent and Weyl symmetric Abelian (Cho-Duan-Ge) decomposition of the SU(3) QCD, and present a new gauge invariant integral expression of the one-loop effective action which has no infrared divergence. Integrating it gauge invariantly imposing the color reflection invariance ("the C-projection") we show that the effective potential generates the stable monopole condensation which generates the mass gap.

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7

ZENKIN, S. V. "GENERAL FORM OF THE LATTICE FERMION ACTION." Modern Physics Letters A 06, no. 02 (January 20, 1991): 151–55. http://dx.doi.org/10.1142/s0217732391000105.

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A set of lattice fermion actions is found which are consistent with canonical quantization of fermion systems. A new type of non-local chirally invariant action determined by the Weyl quantization is found to be inconsistent with gauge invariance. This completes the demonstration of the inconsistency of the non-local actions. The other actions are of the generalized Wilson form and may have the Kogut-Susskind-like symmetry which forbids mass terms.

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8

IRAC-ASTAUD, MICHÈLE. "DIFFERENTIAL CALCULUS ON A THREE-PARAMETER OSCILLATOR ALGEBRA." Reviews in Mathematical Physics 08, no. 08 (November 1996): 1083–90. http://dx.doi.org/10.1142/s0129055x96000408.

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Two differential calculi are developed on an algebra generalizing the usual q-oscillator algebra and involving three generators and three parameters. They are shown to be invariant under the same quantum group that is extended to a ten-generator Hopf algebra. We discuss the special case where it reduces to a deformation of the invariance group of the Weyl-Heisenberg algebra for which we prove the existence of a constraint between the values of the parameters.

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9

HARADA, KOJI. "EQUIVALENCE BETWEEN THE WESS-ZUMINO-WITTEN MODEL AND TWO CHIRAL BOSONS." International Journal of Modern Physics A 06, no. 19 (August 10, 1991): 3399–418. http://dx.doi.org/10.1142/s0217751x91001659.

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We establish the formal equivalence of a bosonized Dirac fermion (the Wess-Zumino-Witten model) to two bosonized Weyl fermions (Sonnenschein’s chiral bosons) in the path integral framework. These two systems can be regarded as gauge-fixed systems of the same gauge-invariant theory. Factorization of the fermion determinant of QCD2 is naturally realized in terms of chiral bosonization, up to a contact term which is necessary for maintaining gauge invariance. Canonical quantization of the gauge-invariantly extended system is performed.

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10

Temme, Francis P. "Commutator-Based (A)[X]n(SU(2)×Sn) NMR Cluster Systems: Establishment of the Universality of [n](Sn) Salients and Constraints on ϕ±11(1.1) Polarisations to the [1n] Salient: Permutational Spin Symmetry (PSS) Within NMR Spin Dynamics - an Analytic View." Collection of Czechoslovak Chemical Communications 70, no. 8 (2005): 1177–95. http://dx.doi.org/10.1135/cccc20051177.

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Analytic SU(2) × Sn dual tensorial (DT) spin dynamics over uniform NMR spins is invoked in examining the modern quantum basis for the universal non-observability rule which governs dominant intracluster JXX' couplings of (A)[X]n NMR systems as a specific form of (abstract) permutational spin symmetry (PSS) with well defined properties on spin-alone space. This is shown to be linked to DT constraints that apply to the cross-product ϕ1±1(1.1) polarisation development i.e., as being confined to [1n](Sn) (Liouvillian) salient, with the existence of [n] (rotating frame) null subspaces. Both these arise within the spin dynamics of (A)[X]2 spin systems (or subsystems thereof) within (a hierarchy of) dominant JXX' governing the internal L(0); such spin systems provide analytic sequels to comparative spin dynamics studies of XX' PSS and AX broken-PSS systems in a Liouvillian coupled tensorial basis formalism, since both draw on (Sanctuary B. C.: Mol. Phys. 1985, 55, 1017), and on the realisation that proper PSS over a (uniform) spin-space L(0) = [H(0),.] zeroth-order Liouvillian and its internal (hierarchical subsets of) JXX' (Temme F. P.: J. Mol. Struct. (THEOCHEM) 2002, 547, 153) i.e., for abstract Sn ↓ G group embeddings. The present work also examines the general irrep-structure of DT spin symmetries for the extent of unit-character irreps and the role of Sn ⊃ Sn-1 ⊃ .. ⊃ [2](S2) group chains in defining the Sn multiple invariants under democratic recoupling of PSS of uniform spin systems. As group measures, these properties apply to both (A)[X]n and [AX]n PSS symmetries, with the invariant cardinality |SI|(n) being related to time-reversal invariance (TRI) and its inherent democratic recoupling (DR) over Weyl (I • I) pairs. For [X]2n uniform spin clusters, |SI|(2n) is best derived via n-fold polyhedral combinatorics of the underlying DR (Temme F. P.: Proc. R. Soc. London, Ser. A 2005, 461, 321) i.e., as an augmented post-Weyl view of the essential role of TRI in (group) invariant cardinality, with the Sn-invariants represented by certain Sn subduction properties.

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11

Fernández Cristóbal, José Ma. "Weyl invariance in metric f(R) gravity." Revista Mexicana de Física 64, no. 2 (March 14, 2018): 181. http://dx.doi.org/10.31349/revmexfis.64.181.

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We aim to derive the most general f(R) gravity theory, including thematter, so that it be Weyl invariant. Making use of the mathematicalequivalence of these theories with an type of scalar-tensor theory, and byimposing the Weyl invariance for the pure gravity as well as for the mattersector, we obtain the fundamental equation that restricts the form of V (phi) (and, accordingly, of f(R)) so that the resulting action to be Weylinvariant in the Jordan frame. We show that this action is not otherthan the so-called dilaton gravity action with one scalar eld,, whicheective mass is R and Phi dependent. In the Einstein frame, the actionbecomes the Einstein-Hilbert action with the Ricci scalar being constantdue to that the eective mass of scalar eld in this frame vanish. So,we can assume that the Ricci scalar, in the Einstein frame, is the trueCosmological Constant. Therefore, is not preposterous to guess that, atleast mathematically, all Weyl invariant metric f(R) theory in the Jordanframe is equivalent, at classical level, to the Einstein gravity, in theEinstein frame, with a constant Ricci scalar. At quantum level, as it isknown, both theories are not equivalent due to the presence of anomaliesin one of the frames.

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12

CLARK, T. E., and S. T. LOVE. "ON LOCAL DILATATION INVARIANCE." Modern Physics Letters A 27, no. 30 (September 26, 2012): 1250174. http://dx.doi.org/10.1142/s021773231250174x.

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The relationship between local Weyl scaling invariant models and local dilatation invariant actions is critically scrutinized. While actions invariant under local Weyl scalings can be constructed in a straightforward manner, actions invariant under local dilatation transformations can only be achieved in a very restrictive case. The invariant couplings of matter fields to an Abelian vector field carrying a nontrivial scaling weight can be easily built, but an invariant Abelian vector kinetic term can only be realized when the local scale symmetry is spontaneously broken.

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13

DAPPIAGGI, CLAUDIO, VALTER MORETTI, and NICOLA PINAMONTI. "RIGOROUS STEPS TOWARDS HOLOGRAPHY IN ASYMPTOTICALLY FLAT SPACETIMES." Reviews in Mathematical Physics 18, no. 04 (May 2006): 349–415. http://dx.doi.org/10.1142/s0129055x0600270x.

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Scalar QFT on the boundary ℑ+at future null infinity of a general asymptotically flat 4D spacetime is constructed using the algebraic approach based on Weyl algebra associated to a BMS-invariant symplectic form. The constructed theory turns out to be invariant under a suitable strongly-continuous unitary representation of the BMS group with manifest meaning when the fields are interpreted as suitable extensions to ℑ+of massless minimally coupled fields propagating in the bulk. The group theoretical analysis of the found unitary BMS representation proves that such a field on ℑ+coincides with the natural wave function constructed out of the unitary BMS irreducible representation induced from the little group Δ, the semidirect product between SO(2) and the two-dimensional translations group. This wave function is massless with respect to the notion of mass for BMS representation theory. The presented result proposes a natural criterion to solve the long-standing problem of the topology of BMS group. Indeed the found natural correspondence of quantum field theories holds only if the BMS group is equipped with the nuclear topology rejecting instead the Hilbert one. Eventually, some theorems towards a holographic description on ℑ+of QFT in the bulk are established at level of C*-algebras of fields for asymptotically flat at null infinity spacetimes. It is proved that preservation of a certain symplectic form implies the existence of an injective *-homomorphism from the Weyl algebra of fields of the bulk into that associated with the boundary ℑ+. Those results are, in particular, applied to 4D Minkowski spacetime where a nice interplay between Poincaré invariance in the bulk and BMS invariance on the boundary at null infinity is established at the level of QFT. It arises that, in this case, the *-homomorphism admits unitary implementation and Minkowski vacuum is mapped into the BMS invariant vacuum on ℑ+.

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14

Arvanitakis, Alex S. "Chiral strings, topological branes, and a generalised Weyl-invariance." International Journal of Modern Physics A 34, no. 06n07 (March 10, 2019): 1950031. http://dx.doi.org/10.1142/s0217751x19500313.

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We introduce a sigma model Lagrangian generalising a number of new and old models which can be thought of as chiral, including the Schild string, ambitwistor strings, and the recently introduced tensionless AdS twistor strings. This “chiral sigma model” describes maps from a [Formula: see text]-brane worldvolume into a symplectic space and is manifestly invariant under diffeomorphisms as well as under a “generalised Weyl invariance” acting on space–time coordinates and worldvolume fields simultaneously. Construction of the Batalin–Vilkovisky master action leads to a BRST operator under which the gauge-fixed action is BRST-exact; we discuss whether this implies that the chiral brane sigma model defines a topological field theory.

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15

AGOSTINI, ALESSANDRA, GIOVANNI AMELINO-CAMELIA, MICHELE ARZANO, and FRANCESCO D'ANDREA. "A CYCLIC INTEGRAL ON κ-MINKOWSKI NONCOMMUTATIVE SPACE–TIME." International Journal of Modern Physics A 21, no. 15 (June 20, 2006): 3133–50. http://dx.doi.org/10.1142/s0217751x06031077.

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We examine some alternative possibilities for an action functional for κ-Minkowski noncommutative space–time. Early works on κ-Minkowski focused on κ-Poincaré covariance and the dependence of the action functional on the choice of Weyl map, renouncing to invariance under cyclic permutations of the factors composing the argument of the action functional. It has been recently suggested, focusing on a specific choice of Weyl map and setting aside the issue of κ-Poincaré covariance of the action functional, that a cyclicity-inducing measure could be introduced in implicit form. We provide an explicit formula for (and derivation of) a choice of measure which indeed ensures cyclicity of the action functional. The same choice of measure is applicable to all the most used choices of Weyl map, but we find that this "cyclicity-inducing measure" is not invariant under κ-Poincaré transformations. We also notice that the cyclicity-inducing measure can be straightforwardly derived using a map which connects the κ-Minkowski space–time coordinates and the space–time coordinates of a "canonical" noncommutative space–time, with coordinate-independent commutators.

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16

Iorio, A., L. O'Raifeartaigh, I. Sachs, and C. Wiesendanger. "Weyl gauging and conformal invariance." Nuclear Physics B 495, no. 1-2 (June 1997): 433–50. http://dx.doi.org/10.1016/s0550-3213(97)00190-9.

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17

Gover, A. R., A. Shaukat, and A. Waldron. "Tractors, mass, and Weyl invariance." Nuclear Physics B 812, no. 3 (May 2009): 424–55. http://dx.doi.org/10.1016/j.nuclphysb.2008.11.026.

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18

Zaikov, R. P. "Conformal invariance in Weyl gravity." International Journal of Theoretical Physics 26, no. 6 (June 1987): 537–48. http://dx.doi.org/10.1007/bf00670092.

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19

Dabholkar, Atish. "Quantum Weyl invariance and cosmology." Physics Letters B 760 (September 2016): 31–35. http://dx.doi.org/10.1016/j.physletb.2016.06.034.

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20

FUJIWARA, TAKANORI, YUJI IGARASHI, and JISUKE KUBO. "WEYL INVARIANCE AND SPURIOUS BLACK HOLES IN TWO-DIMENSIONAL DILATON GRAVITY." International Journal of Modern Physics A 09, no. 27 (October 30, 1994): 4811–35. http://dx.doi.org/10.1142/s0217751x94001953.

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In two-dimensional dilaton gravity theories, there may exist a global Weyl invariance which makes the black hole spurious. If the global invariance and the local Weyl invariance of the matter coupling are intact at the quantum level, there is no Hawking radiation. We explicitly verify the absence of anomalies in these symmetries for the model proposed by Callan, Giddings, Harvey and Strominger. The crucial observation is that the conformal anomaly can be cohomologically trivial and so not truly anomalous in such dilaton gravity models.

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21

BIZDADEA, C., E. M. CIOROIANU, and A. C. LUNGU. "NO INTERACTIONS FOR A COLLECTION OF WEYL GRAVITONS INTERMEDIATED BY A SCALAR FIELD." International Journal of Modern Physics A 21, no. 19n20 (August 10, 2006): 4083–126. http://dx.doi.org/10.1142/s0217751x06031284.

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The cross-couplings among several Weyl gravitons (described in the free limit by a sum of linearized Weyl actions) in the presence of a scalar field are studied with the help of the deformation theory based on local BRST cohomology. Under the hypotheses of locality, smoothness of the interactions in the coupling constant, Poincaré invariance, (background) Lorentz invariance, and the preservation of the number of derivatives on each field, together with the supplementary assumption that the internal metric defined by the sum of Weyl Lagrangians is positively defined, we prove that there are no consistent cross-interactions among different Weyl gravitons in the presence of a scalar field. The couplings of a single Weyl graviton to a scalar field are also discussed.

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22

Poulis, F. P., and J. M. Salim. "Weyl geometry and gauge-invariant gravitation." International Journal of Modern Physics D 23, no. 11 (October 2014): 1450091. http://dx.doi.org/10.1142/s0218271814500916.

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In this paper, we provide a gauge-invariant theory of gravitation in the context of Weyl Integrable Spacetimes. After making a brief review of the theory's postulates, we carefully define the observers' proper-time and point out its relation with spacetime description. As a consequence of this relation and the theory's gauge symmetry we recover all predictions of general relativity. This feature is made even clearer by a new exact solution we provide which reveals the importance of a well defined proper-time. The thermodynamical description of the source fields is given and we observe that each of the geometric fields have a certain physical significance, despite the gauge-invariance. This is shown by two examples, where one of them consists of a new cosmological constant solution. Our conclusions highlight the intimate relation among test particles trajectories, proper-time and spacetime description which can also be applied in any other situation, whether or not it recovers general relativity results and also in the absence of a gauge symmetry.

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23

MOON, TAEYOON, JOOHAN LEE, and PHILLIAL OH. "CONFORMAL INVARIANCE IN EINSTEIN–CARTAN–WEYL SPACE." Modern Physics Letters A 25, no. 37 (December 7, 2010): 3129–43. http://dx.doi.org/10.1142/s0217732310034201.

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We consider conformally invariant form of the actions in Einstein, Weyl, Einstein–Cartan and Einstein–Cartan–Weyl space in general dimensions (> 2) and investigate the relations among them. In Weyl space, the observational consistency condition for the vector field determining non-metricity of the connection can be obtained from the equation of motion. In Einstein–Cartan space a similar role is played by the vector part of the torsion tensor. We consider the case where the trace part of the torsion is the Kalb–Ramond type of field. In this case, we express conformally invariant action in terms of two scalar fields of conformal weight -1, which can be cast into some interesting form. We discuss some applications of the result.

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24

Temme, F. P. "On spin irreps of (1 Ii 3) 12-fold uniform NMR spin systems as invariant-based dual tensorial sets: Roles in spin physics for weight sets and their -partitional frequency catalogues." Canadian Journal of Physics 80, no. 9 (September 1, 2002): 1069–83. http://dx.doi.org/10.1139/p02-005.

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A direct systematic approach is given to the derivation of outer M-labelled {|IM(.)>} dual (spin) irrep sets for identical n [Formula: see text] 12-fold higher Ii nuclear spin ensembles, stressing (i) the essential role of multipartite partitions in spin physics, (ii) the value of algorithmic tableaux-based decompositions in the subsequent [Formula: see text]n combinatorical modelling, and (iii) how the dual group invariants (based on time-reversal invariance) govern the auxiliary labels of specialized dual tensors. Such (uniform inner rank) dual group basis sets (spin representations) underlie both NMR and isotopomer CNP spectral weightings. Specific applications are discussed here to illustrate the value of number partitional-based designs for statistical frequencies and recent algorithmic "sst" ([Formula: see text]n)-encoding techniques in quantized spin physics of uniform higher spin sets. In addition, a democratic recoupled form of purely SU(2) × [Formula: see text]2n projective modelling for the dual group invariants (SI) is given via an augmented democratic form of Weyl time-reversal invariance (TRV), over some regular solid geometry. From simple lattice-point geometric constraints, a maximal (2n)-index limit is established for global NMR ensemble spin symmetry. PACS Nos.: 02.10De, 02.20-a, 05.36Ch, 11.30Er, 33.25+k, 33.20Vq

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25

DE ANDRADE, M. A., and O. M. DEL CIMA. "SUPER-τ3QED AND THE DIMENSIONAL REDUCTION OF N=1SUPER-QED2+2." International Journal of Modern Physics A 11, no. 08 (March 30, 1996): 1367–89. http://dx.doi.org/10.1142/s0217751x96000638.

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In this work the supersymmetric gauge-invariant action for the massive Abelian N=1 super-QED 2+2 in the Atiyah-Ward space-time (D=2+2) is formulated. The questions concerning the scheme of the gauge invariance in D=2+2 by means of gauging the massive N=1 super-QED 2+2 are investigated. We study how to ensure the gauge invariance at the expense of the introduction of a complex vector superfield. We discuss the Wess-Zumino gauge and thereupon we conclude that, in this gauge, only the imaginary part of the complex vector field, Bμ, gauges a U(1) symmetry. whereas its real part gauges a Weyl symmetry. We build up the gauge-invariant massive term by introducing a pair of chiral and antichiral superfields with opposite U(1) charges. We carry out a dimensional reduction à la Scherk of the massive N=1 super-QED 2+2 action from D=2+2 to D=1+2. Truncations are needed in order to suppress nonphysical modes, and we end up with a parity-preserving N=1 super-QED 1+2 (rather than N=2) in D=1+2. Finally, we show that the N=1 super-QED 1+2 we have obtained is the supersymmetric version of τ3 QED .

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26

Hosotani, Y. "Weyl Invariant Spacetime." Progress of Theoretical Physics 109, no. 2 (February 1, 2003): 295–303. http://dx.doi.org/10.1143/ptp.109.295.

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27

Alvarez, Enrique, Sergio González-Martín, and Mario Herrero-Valea. "Some cosmological consequences of Weyl invariance." Journal of Cosmology and Astroparticle Physics 2015, no. 03 (March 19, 2015): 035. http://dx.doi.org/10.1088/1475-7516/2015/03/035.

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28

Kuzenko, Sergei M., and Gabriele Tartaglino-Mazzucchelli. "Super-Weyl invariance in 5D supergravity." Journal of High Energy Physics 2008, no. 04 (April 10, 2008): 032. http://dx.doi.org/10.1088/1126-6708/2008/04/032.

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29

Zhao, Shu-Cheng, and Duan Yishi. "Conformal (Weyl) invariance and Higgs mechanism." Il Nuovo Cimento A 105, no. 12 (December 1992): 1739–43. http://dx.doi.org/10.1007/bf02740923.

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30

Jain, Sanjay, and A. Jevicki. "String field theory from Weyl invariance." Physics Letters B 220, no. 3 (April 1989): 379–86. http://dx.doi.org/10.1016/0370-2693(89)90891-5.

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31

Navarro-Salas, J., M. Navarro, and C. F. Talavera. "Weyl invariance and black hole evaporation." Physics Letters B 356, no. 2-3 (August 1995): 217–22. http://dx.doi.org/10.1016/0370-2693(95)00848-f.

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32

Codello, A., G. D’Odorico, C. Pagani, and R. Percacci. "The renormalization group and Weyl invariance." Classical and Quantum Gravity 30, no. 11 (May 13, 2013): 115015. http://dx.doi.org/10.1088/0264-9381/30/11/115015.

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33

MELJANAC, S., and A. SAMSAROV. "SCALAR FIELD THEORY ON κ-MINKOWSKI SPACE–TIME AND TRANSLATION AND LORENTZ INVARIANCE." International Journal of Modern Physics A 26, no. 07n08 (March 30, 2011): 1439–68. http://dx.doi.org/10.1142/s0217751x11051536.

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We investigate the properties of κ-Minkowski space–time by using representations of the corresponding deformed algebra in terms of undeformed Heisenberg–Weyl algebra. The deformed algebra consists of κ-Poincaré algebra extended with the generators of the deformed Weyl algebra. The part of deformed algebra, generated by rotation, boost and momentum generators, is described by the Hopf algebra structure. The approach used in our considerations is completely Lorentz covariant. We further use an advantage of this approach to consistently construct a star product, which has a property that under integration sign, it can be replaced by a standard pointwise multiplication, a property that was since known to hold for Moyal but not for κ-Minkowski space–time. This star product also has generalized trace and cyclic properties, and the construction alone is accomplished by considering a classical Dirac operator representation of deformed algebra and requiring it to be Hermitian. We find that the obtained star product is not translationally invariant, leading to a conclusion that the classical Dirac operator representation is the one where translation invariance cannot simultaneously be implemented along with hermiticity. However, due to the integral property satisfied by the star product, noncommutative free scalar field theory does not have a problem with translation symmetry breaking and can be shown to reduce to an ordinary free scalar field theory without nonlocal features and tachyonic modes and basically of the very same form. The issue of Lorentz invariance of the theory is also discussed.

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34

HAMADA, KEN-JI. "CONFORMAL FIELD THEORY ON R × S3 FROM QUANTIZED GRAVITY." International Journal of Modern Physics A 24, no. 16n17 (July 10, 2009): 3073–110. http://dx.doi.org/10.1142/s0217751x0904422x.

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Conformal algebra on R × S3 derived from quantized gravitational fields is examined. The model we study is a renormalizable quantum theory of gravity in four dimensions described by a combined system of the Weyl action for the traceless tensor mode and the induced Wess–Zumino action managing nonperturbative dynamics of the conformal factor in the metric field. It is shown that the residual diffeomorphism invariance in the radiation+ gauge is equal to the conformal symmetry, and the conformal transformation preserving the gauge-fixing condition that forms a closed algebra quantum mechanically is given by a combination of naive conformal transformation and a certain field-dependent gauge transformation. The unitarity issue of gravity is discussed in the context of conformal field theory. We construct physical states by solving the conformal invariance condition and calculate their scaling dimensions. It is shown that the conformal symmetry mixes the positive-metric and the negative-metric modes and thus the negative-metric mode does not appear independently as a gauge invariant state at all.

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35

GRUMILLER, D., D. HOFMANN, and W. KUMMER. "2D GRAVITY WITHOUT TEST PARTICLES IS POINTLESS." Modern Physics Letters A 16, no. 24 (August 10, 2001): 1597–600. http://dx.doi.org/10.1142/s0217732301004935.

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36

MIYATA, HIDEO, and NORIYASU OHTSUBO. "WEYL ORBIFOLD MODELS." Modern Physics Letters A 11, no. 28 (September 14, 1996): 2285–96. http://dx.doi.org/10.1142/s0217732396002277.

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Superstring models on Weyl orbifolds are investigated in [Formula: see text] heterotic string theories. Some of the Weyl orbifold models are shown to be consistent with worldsheet supersymmetry, N=1 spacetime supersymmetry and modular invariance. Two ways of embedding in [Formula: see text] are studied and residual gauge groups are classified.

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37

FAN, HONG-YI. "INVARIANCE OF WEYL ORDERING OF FERMI OPERATORS UNDER SIMILAR TRANSFORMATIONS." Modern Physics Letters A 21, no. 10 (March 28, 2006): 809–20. http://dx.doi.org/10.1142/s0217732306019025.

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A Weyl–Wigner quantization scheme for Fermi system which is parallel to the bosonic case is established. We prove a new theorem: Weyl ordering of Fermi operators is invariant under fermionic similar transformations. Comparing with the preceding paper,1 we see the Bose–Fermi supersymmetry in this aspect. As an application of the theorem, we construct a generalized fermionic squeezed state.

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38

KATOK, A., and R. J. SPATZIER. "Corrections to ‘Invariant measures for higher-rank hyperbolic abelian actions’." Ergodic Theory and Dynamical Systems 18, no. 2 (April 1998): 503–7. http://dx.doi.org/10.1017/s0143385798110969.

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The proofs of Theorems 5.1 and 7.1 of [2] contain a gap. We will show below how to close it under some suitable additional assumptions in these theorems and their corollaries. We will assume the notation of [2] throughout. In particular, $\mu$ is a measure invariant and ergodic under an $R^k$-action $\alpha$. Let us first explain the gap. Both theorems are proved by establishing a dichotomy for the conditional measures of $\mu$ along the intersection of suitable stable manifolds. They were either atomic or invariant under suitable translation or unipotent subgroups $U$. Atomicity eventually led to zero entropy. Invariance of the conditional measures showed invariance of $\mu$ under $U$. We then claimed that $\mu$ was algebraic using, respectively, unique ergodicity of the translation subgroup on a rational subtorus or Ratner's theorem (cf. [2, Lemma 5.7]). This conclusion, however, only holds for the $U$-ergodic components of $\mu$ which may not equal $\mu$. In fact, in the toral case, the $R^k$-action may have a zero-entropy factor such that the conditional measures along the fibers are Haar measures along a foliation by rational subtori. Since invariant measures with zero entropy have not been classified, we cannot conclude algebraicity of the total measure $\mu$ at this time. In the toral case, the existence of zero entropy factors turns out to be precisely the obstruction to our methods. The case of Weyl chamber flows is somewhat different as the ‘Haar’ direction of the measure may not be integrable. In this case, we need to use additional information coming from the semisimplicity of the ambient Lie group to arrive at the versions of Theorem 7.1 presented below.

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39

FAN, HONG-YI, and JI-SUO WANG. "ON THE WEYL ORDERING INVARIANCE UNDER GENERAL n-MODE SIMILAR TRANSFORMATIONS." Modern Physics Letters A 20, no. 20 (June 28, 2005): 1525–32. http://dx.doi.org/10.1142/s0217732305017512.

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We reveal that Weyl ordering of operators is invariant under general n-mode similar transformations. The technique of integration within a Weyl ordered product of operators is employed to prove our statement. Application of this property in obtaining generalized squeezed state via similar transformation is discussed.

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40

Coumbe, Daniel. "Asymptotically Weyl-invariant gravity." International Journal of Modern Physics A 34, no. 31 (November 10, 2019): 1950205. http://dx.doi.org/10.1142/s0217751x19502051.

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We propose a novel theory of gravity that by construction is renormalizable, evades Ostrogradsky’s no-go theorem, is locally scale-invariant in the high-energy limit, and equivalent to general relativity in the low-energy limit. The theory is defined by a pure [Formula: see text] action in the Palatini formalism, where the dimensionless exponent [Formula: see text] runs from a value of two in the high-energy limit to one in the low-energy limit. We show that the proposed model contains no obvious cosmological curvature singularities. The viability of the proposed model is qualitatively assessed using several key criteria.

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Kao, W. F., Shi-Yuun Lin, and Tzuu-Kang Chyi. "Weyl invariant black hole." Physical Review D 53, no. 4 (February 15, 1996): 1955–62. http://dx.doi.org/10.1103/physrevd.53.1955.

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42

Savvidy, G. K., and R. Manvelyan. "Weyl invariant gonihedric strings." Physics Letters B 533, no. 1-2 (May 2002): 138–45. http://dx.doi.org/10.1016/s0370-2693(02)01557-5.

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43

Temme, F. P. "Geodesic and re–coupling–induced limits to S 2 n group invariants of uniform ( k 1 ⋯ k 2 n ) dual tensorial sets in spin physics, or NMR: SR dynamical structure on {ℍ v } via polyhedral re–coupling and time–reversal invariance." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2054 (February 8, 2005): 321–46. http://dx.doi.org/10.1098/rspa.2004.1323.

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For S n –based, uniform auxiliary dual tensorial (UDT) sets, explicitly with even maximal all–alike j i ( k i ) over v ≡ ( j 1 ⋯ j 2 n ), or ( k 1 ⋯ k 2 n ), sub–rank auxiliary labelling, the specific time–reversal invariance–dependent dual group invariants and their independent cardinalities (| SI | (2 n ) ) are fundamental to understanding simply reducible (SR) dynamical spin system structure over (Liouvillian) carrier space, a quantum physics property implicit in dual quasi–particle (QP) formalisms associated with, for example, uniform identical multiple spin NMR systems . Such UDT sets stand in total contrast to the distinct j i ( k i ) of ( j 1 ⋯ j″ n )(( k 1 ⋯ k″ n )) sub–rank orthogonal tensorial sets with their Z aa′ graph invariants which for reasons discussed in the text are of restricted validity. For UDTs as operator bases related to the (spin) interaction network–based tensors of high S n permutational NMR Hamiltonians (Liouvillians), the use of QP boson (superboson) formalisms and their dual projective maps (F. P. Temme 1993 Physica A 198 , 245–261) prove invaluable. Once the independent cardinality of the multiple invariants of these UDTs (alias the SU (2) × S 2 n group invariants) (here denoted | SI | (2 n ) ) are known in terms of democratic re–coupling (DR) and polyhedral combinatorial (PC) sampling applied to the time–reversal invariance (TRI) properties of the uniform multiple spin (sub–)system, so the SR dual carrier spaces , ℍ˜, ℍ˜ v follow directly as well–defined entities. For UDTs of general (2 n > 6)–fold ensembles, the augmented models of TRI discussed here (i.e. beyond linear re–coupled Weyl forms) are essential, due to the presence of non–Abelian degeneracy. A regular geometric automorphic limit is established for sequential (2 n )–based | SI | (2 n ) total series, specific to (higher) uniform ( j 1 ⋯ j i ), ( k 1 ⋯ k i )–based dual tensors. By treating the | SI | (2 n ) obtained from the DR–based TRIs as group measures and invoking an automorphic geodesic augmentation, certain otherwise inaccessible, additional | SI | (2 n′ ) (and hence UDTs) may be established; these are based on sporadic higher (regular) (2 n ≫ 12)–fold ensemble invariants and are obtained via finite group duality properties implicit in the concept of group measures. The PC DR–based views of general (2 n ) interacting spins of UDTs expressed here give specific insight into dynamic structure over (explicit TRI invariant–defined) Liouvillian carrier spaces. This lattice point (Erdösian) view of DR shows that UDT invariants are distinct and more contracted than predicted by the earlier linear–re–coupling–based | D 0 ( U )|(⨷ SU (2)) approach. The presence of degeneracy in general high (2 n ) UDTs as non–Abelian entities ensures that the homomorphic–based, | D 0 ( U )| enumeration (with its implied linear graphical re–coupling) is invalid for high (2 n ) uniform (NMR) multi–spin systems whose TRI properties are governed by DR re–coupling. The prime focus of the report concerns the positive conceptual value of PC lattice–point–based DR, as applied to the S 2 n –invariants which define UDTs (of NMR) and their completeness. Brief contrasts with the earlier, more restricted O (2 k + 1) (overall) invariants of ( O ( n ) ⊃ ⋯ ⊃ G )–based democratic re–coupled quantum systems are given for completeness.

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Zhang, Nan, Gan Zhao, Lin Li, Pengdong Wang, Lin Xie, Bin Cheng, Hui Li, et al. "Magnetotransport signatures of Weyl physics and discrete scale invariance in the elemental semiconductor tellurium." Proceedings of the National Academy of Sciences 117, no. 21 (May 12, 2020): 11337–43. http://dx.doi.org/10.1073/pnas.2002913117.

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The study of topological materials possessing nontrivial band structures enables exploitation of relativistic physics and development of a spectrum of intriguing physical phenomena. However, previous studies of Weyl physics have been limited exclusively to semimetals. Here, via systematic magnetotransport measurements, two representative topological transport signatures of Weyl physics, the negative longitudinal magnetoresistance and the planar Hall effect, are observed in the elemental semiconductor tellurium. More strikingly, logarithmically periodic oscillations in both the magnetoresistance and Hall data are revealed beyond the quantum limit and found to share similar characteristics with those observed in ZrTe5and HfTe5. The log-periodic oscillations originate from the formation of two-body quasi-bound states formed between Weyl fermions and opposite charge centers, the energies of which constitute a geometric series that matches the general feature of discrete scale invariance (DSI). Our discovery reveals the topological nature of tellurium and further confirms the universality of DSI in topological materials. Moreover, introduction of Weyl physics into semiconductors to develop “Weyl semiconductors” provides an ideal platform for manipulating fundamental Weyl fermionic behaviors and for designing future topological devices.

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45

De Martini, Francesco, and Enrico Santamato. "Proof of the spin-statistics theorem in the relativistic regimen by Weyl’s conformal quantum mechanics." International Journal of Quantum Information 14, no. 04 (June 2016): 1640011. http://dx.doi.org/10.1142/s0219749916400116.

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The traditional standard theory of quantum mechanics is unable to solve the spin-statistics problem, i.e. to justify the utterly important “Pauli Exclusion Principle” but by the adoption of the complex standard relativistic quantum field theory. In a recent paper [E. Santamato and F. D. De Martini, Found. Phys. 45 (2015) 858] we presented a complete proof of the spin-statistics problem in the nonrelativistic approximation on the basis of the “Conformal Quantum Geometrodynamics” (CQG). In this paper, by the same theory, the proof of the spin-statistics theorem (SST) is extended to the relativistic domain in the scenario of curved spacetime. No relativistic quantum field operators are used in the present proof and the particle exchange properties are drawn from rotational invariance rather than from Lorentz invariance. Our relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. As in the nonrelativistic case, we find once more that the “intrinsic helicity” of the elementary particles enters naturally into play. It is therefore this property, not considered in the standard quantum mechanics (SQM), which determines the correct spin-statistics connection observed in Nature.

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46

Háková, Lenka, and Agnieszka Tereszkiewicz. "ON GENERALIZATION OF SPECIAL FUNCTIONS RELATED TO WEYL GROUPS." Acta Polytechnica 56, no. 6 (December 31, 2016): 440–47. http://dx.doi.org/10.14311/ap.2016.56.0440.

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Weyl group orbit functions are defined in the context of Weyl groups of simple Lie algebras. They are multivariable complex functions possessing remarkable properties such as (anti)invariance with respect to the corresponding Weyl group, continuous and discrete orthogonality. A crucial tool in their definition are so-called sign homomorphisms, which coincide with one-dimensional irreducible representations. In this work we generalize the definition of orbit functions using characters of irreducible representations of higher dimensions. We describe their properties and give examples for Weyl groups of rank 2 and 3.

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47

Álvarez, Enrique, and Sergio González-Martín. "Weyl invariance with a nontrivial mass scale." Journal of Cosmology and Astroparticle Physics 2016, no. 09 (September 7, 2016): 012. http://dx.doi.org/10.1088/1475-7516/2016/09/012.

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48

Gover, A. R., A. Shaukat, and A. Waldron. "Weyl invariance and the origins of mass." Physics Letters B 675, no. 1 (May 2009): 93–97. http://dx.doi.org/10.1016/j.physletb.2009.03.072.

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49

Lü, H., C. N. Pope, and K. S. Stelle. "Weyl group invariance and p-brane multiplets." Nuclear Physics B 476, no. 1-2 (September 1996): 89–117. http://dx.doi.org/10.1016/0550-3213(96)00264-7.

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50

Dewar, Neil, and James Read. "Conformal Invariance of the Newtonian Weyl Tensor." Foundations of Physics 50, no. 11 (October 6, 2020): 1418–25. http://dx.doi.org/10.1007/s10701-020-00386-w.

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AbstractIt is well-known that the conformal structure of a relativistic spacetime is of profound physical and conceptual interest. In this note, we consider the analogous structure for Newtonian theories. We show that the Newtonian Weyl tensor is an invariant of this structure.

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