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Journal articles on the topic 'Unitarist construct'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

AHUJA, GULSHEEN. "EXPLORING THE LIKELIHOOD OF CP VIOLATION IN NEUTRINO OSCILLATIONS." Modern Physics Letters A 26, no. 34 (November 10, 2011): 2597–603. http://dx.doi.org/10.1142/s0217732311036905.

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In view of the latest T2K and MINOS observations regarding the mixing angle s13, we have explored the possibility of the existence of CP violation in the leptonic sector. Using hints from the construction of the "db" unitarity triangle in the quark sector, we have made an attempt to construct the "ν1⋅ν3" leptonic unitarity triangle, suggesting a good possibility of having nonzero CP violation.

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2

Arveson, William. "The noncommutative Choquet Boundary III." MATHEMATICA SCANDINAVICA 106, no. 2 (June 1, 2010): 196. http://dx.doi.org/10.7146/math.scand.a-15132.

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We classify operator systems $S\subseteq \mathcal{B}(H)$ that act on finite dimensional Hilbert spaces $H$ by making use of the noncommutative Choquet boundary. $S$ is said to be reduced when its boundary ideal is $\{0\}$. In the category of operator systems, that property functions as semisimplicity does in the category of complex Banach algebras. We construct explicit examples of reduced operator systems using sequences of "parameterizing maps" $\Gamma_k: \mathsf{C}^r\to \mathcal{B}(H_k)$, $k=1,\dots, N$. We show that every reduced operator system is isomorphic to one of these, and that two sequences give rise to isomorphic operator systems if and only if they are "unitarily equivalent" parameterizing sequences. Finally, we construct nonreduced operator systems $S$ that have a given boundary ideal $K$ and a given reduced image in $C^*(S)/K$, and show that these constructed examples exhaust the possibilities.

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3

Kamiński, Robert. "Methods of parameterization of amplitudes and extraction of resonances, D-decay amplitudes." EPJ Web of Conferences 212 (2019): 02008. http://dx.doi.org/10.1051/epjconf/201921202008.

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Amplitudes used for analyses of two-body interactions very often are not unitary therefore can not guarantee correct results. It is, however, quite easy to construct unitary amplitude or check whether given amplitude fulfills unitarity condition. Only few conditions must be fulfilled to guarantee unitarity. Presently, when in many data analyses very small, overlapping or broad signals are studied, non-unitary effects can significantly influence results and lead to nonphysical interpretation of obtained parameters.

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4

Enock, Michel. "QUANTUM GROUPOIDS OF COMPACT TYPE." Journal of the Institute of Mathematics of Jussieu 4, no. 1 (January 2005): 29–133. http://dx.doi.org/10.1017/s1474748005000022.

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To any groupoid, equipped with a Haar system, Jean-Michel Vallin had associated several objects (pseudo-multiplicative unitary, Hopf-bimodule) in order to generalize, up to the groupoid case, the classical notions of multiplicative unitary and Hopf–von Neumann algebra, which were intensely used to construct quantum groups in the operator algebra setting. In two former articles (one in collaboration with Jean-Michel Vallin), starting from a depth-2 inclusion of von Neumann algebras, we have constructed such objects, which allowed us to study two ‘quantum groupoids’ dual to each other. We are now investigating in greater details the notion of pseudo-multiplicative unitary, following the general strategy developed by Baaj and Skandalis for multiplicative unitaries. AMS 2000 Mathematics subject classification: Primary 46L89; 22A22; 81R50

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5

Muić, Goran. "On Certain Classes of Unitary Representations for Split Classical Groups." Canadian Journal of Mathematics 59, no. 1 (February 1, 2007): 148–85. http://dx.doi.org/10.4153/cjm-2007-007-0.

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AbstractIn this paper we prove the unitarity of duals of tempered representations supported onminimal parabolic subgroups for split classical p-adic groups. We also construct a family of unitary spherical representations for real and complex classical groups.

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6

Arthur, Winfred, David J. Woehr, and Robyn Maldegen. "Convergent and Discriminant Validity of Assessment Center Dimensions: A Conceptual and Empirical Reexamination of the Assessment Center Construct-Related Validity Paradox." Journal of Management 26, no. 4 (August 2000): 813–35. http://dx.doi.org/10.1177/014920630002600410.

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This study notes that the lack of convergent and discriminant validity of assessment center ratings in the presence of content-related and criterion-related validity is paradoxical within a unitarian framework of validity. It also empirically demonstrates an application of generalizability theory to examining the convergent and discriminant validity of assessment center dimensional ratings. Generalizability analyses indicated that person, dimension, and person by dimension effects contribute large proportions of variance to the total variance in assessment center ratings. Alternately, exercise, rater, person by exercise, and dimension by exercise effects are shown to contribute little to the total variance. Correlational and confirmatory factor analyses results were consistent with the generalizability results. This provides strong evidence for the convergent and discriminant validity of the assessment center dimension ratings–a finding consistent with the conceptual underpinnings of the unitarian view of validity and inconsistent with previously reported results. Implications for future research and practice are discussed.

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7

QUANO, YAS-HIRO. "GENERALIZED SKLYANIN ALGEBRA AND INTEGRABLE LATTICE MODELS." International Journal of Modern Physics A 09, no. 13 (May 20, 1994): 2245–81. http://dx.doi.org/10.1142/s0217751x94000935.

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We study three properties of the ℤn⊗ℤn-symmetric lattice model; i.e. the initial condition, the unitarity and the crossing symmetry. The scalar factors appearing in the unitarity and the crossing symmetry are explicitly obtained. The [Formula: see text]-Sklyanin algebra is introduced in the natural framework of the inverse problem for this model. We build both finite- and infinite-dimensional representations of the [Formula: see text]-Sklyanin algebra, and construct an [Formula: see text] generalization of the broken ℤN model. Furthermore, the Yang-Baxter equation for this new model is proved.

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8

Cao, Lei, and Selcuk Koyuncu. "A note on multilevel Toeplitz matrices." Special Matrices 7, no. 1 (January 1, 2019): 114–26. http://dx.doi.org/10.1515/spma-2019-0011.

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Abstract Chien, Liu, Nakazato and Tam proved that all n × n classical Toeplitz matrices (one-level Toeplitz matrices) are unitarily similar to complex symmetric matrices via two types of unitary matrices and the type of the unitary matrices only depends on the parity of n. In this paper we extend their result to multilevel Toeplitz matrices that any multilevel Toeplitz matrix is unitarily similar to a complex symmetric matrix. We provide a method to construct the unitary matrices that uniformly turn any multilevel Toeplitz matrix to a complex symmetric matrix by taking tensor products of these two types of unitary matrices for one-level Toeplitz matrices according to the parity of each level of the multilevel Toeplitz matrices. In addition, we introduce a class of complex symmetric matrices that are unitarily similar to some p-level Toeplitz matrices.

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9

DOBREV, V. K., and E. SEZGIN. "A REMARKABLE REPRESENTATION OF THE SO(3, 2) KAC-MOODY ALGEBRA." International Journal of Modern Physics A 06, no. 26 (November 10, 1991): 4699–719. http://dx.doi.org/10.1142/s0217751x91002239.

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We construct a minimal representation of the SO(3, 2) Kac-Moody algebra which is based on the spin-zero singleton (the Rac) representation of SO(3, 2). The representation is minimal in the sense that the central charge k of the SO(3, 2) Kac-Moody algebra is chosen to take the special value of [Formula: see text], which allows imposition of the maximum number of reducibility conditions. For the Rac, this is the unique choice for the remarkable property of maximum reducibility which is consistent with unitarity. To ensure unitarity, we furthermore impose an invariance condition under the maximal compact subalgebra SO(3) × SO(2).

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10

THIRRING, W., and N. NARNHOFER. "COVARIANT QED WITHOUT INDEFINITE METRIC." Reviews in Mathematical Physics 04, spec01 (December 1992): 197–211. http://dx.doi.org/10.1142/s0129055x92000200.

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We construct for the linearized Higgs model a representation of the field operators in a Hilbert space ℋ with the following features: ℋ has a positive definite metric but is nonseparable. The vacuum is gauge invariant. The gauge variant operators exist only in their exponentiated form as unitaries. There is a subspace of ℋ where [Formula: see text] is represented by 0.

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11

LIU, SHUDONG, and XIAOCHUN FANG. "EXTENSION ALGEBRAS OF CUNTZ ALGEBRA, II." Bulletin of the Australian Mathematical Society 80, no. 1 (June 8, 2009): 83–90. http://dx.doi.org/10.1017/s0004972709000227.

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AbstractIn this paper, we construct the unique (up to isomorphism) extension algebra, denoted by E∞, of the Cuntz algebra 𝒪∞ by the C*-algebra of compact operators on a separable infinite-dimensional Hilbert space. We prove that two unital monomorphisms from E∞ to a unital purely infinite simple C*-algebra are approximately unitarily equivalent if and only if they induce the same homomorphisms in K-theory.

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12

Mezher, Rawad, Joe Ghalbouni, Joseph Dgheim, and Damian Markham. "On Unitary t-Designs from Relaxed Seeds." Entropy 22, no. 1 (January 12, 2020): 92. http://dx.doi.org/10.3390/e22010092.

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The capacity to randomly pick a unitary across the whole unitary group is a powerful tool across physics and quantum information. A unitary t-design is designed to tackle this challenge in an efficient way, yet constructions to date rely on heavy constraints. In particular, they are composed of ensembles of unitaries which, for technical reasons, must contain inverses and whose entries are algebraic. In this work, we reduce the requirements for generating an ε -approximate unitary t-design. To do so, we first construct a specific n-qubit random quantum circuit composed of a sequence of randomly chosen 2-qubit gates, chosen from a set of unitaries which is approximately universal on U ( 4 ) , yet need not contain unitaries and their inverses nor are in general composed of unitaries whose entries are algebraic; dubbed r e l a x e d seed. We then show that this relaxed seed, when used as a basis for our construction, gives rise to an ε -approximate unitary t-design efficiently, where the depth of our random circuit scales as p o l y ( n , t , l o g ( 1 / ε ) ) , thereby overcoming the two requirements which limited previous constructions. We suspect the result found here is not optimal and can be improved; particularly because the number of gates in the relaxed seeds introduced here grows with n and t. We conjecture that constant sized seeds such as those which are usually present in the literature are sufficient.

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13

Nguyen Thi Kim, Ha, Van Nguyen Thi Hong, and Son Cao Van. "Unitarity of neutrino mixing matrix." EPJ Web of Conferences 206 (2019): 09009. http://dx.doi.org/10.1051/epjconf/201920609009.

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Neutrinos are neutral leptons and there exist three types of neutrinos (electron neutrinos νe, muon neutrinos νµ and tau neutrinos ντ). These classifications are referred to as neutrinos’s “flavors”. Oscillations between the different flavors are known as neutrino oscillations, which occurs when neutrinos have mass and non-zero mixing. Neutrino mixing is governed by the PMNS mixing matrix. The PMNS mixing matrix is constructed as the product of three independent rotations. With that, we can describe the numerical parameters of the matrix in a graphical form called the unitary triangle, giving rise to CP violation. We can calculate the four parameters of the mixing matrix to draw the unitary triangle. The area of the triangle is a measure of the amount of CP violation.

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14

Aguado Benito, José Antonio, Emilia Beniro Roldán, and Josué García Herrero. "Cómo construir una viga gaviota. Miguel Fisac: una idea experimental." Constelaciones. Revista de Arquitectura de la Universidad CEU San Pablo, no. 8 (May 1, 2020): 47–63. http://dx.doi.org/10.31921/constelaciones.n8a3.

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En el anteproyecto de la Iglesia de San Esteban Protomártir Miguel Fisacmuestra por vez primera uno de los elementos singulares de su arquitectura: las vigas gaviota. Se propone una revisión de esta solución, enigmática y malograda, a la luz de la documentación inédita de los proyectos del Colegio del Espíritu Santo en Calahorra y la Iglesia para la Ciudad de los Niños en Costa Rica.Aunque nunca llegan a construirse, las vigas gaviota representan un eslabón imprescindible en la línea evolutiva del grupo de elementos unitarios en hormigón de Fisac, desde los pórticos, marquesinas y pérgolas iniciales a las vigas hueso.El estudio directo de la documentación original de los proyectos mencionados nos permite establecer una hipótesis razonada sobre la manera en que Fisac pensaba ejecutarlas, incógnita que encontraría respuesta, como en otras ocasiones de su obra, en la tradición constructiva autóctona.

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15

TANIMURA, SHOGO. "QUANTIZATION ON A TORUS WITHOUT POSITION OPERATORS." Modern Physics Letters A 18, no. 38 (December 14, 2003): 2755–65. http://dx.doi.org/10.1142/s0217732303012301.

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We formulate quantum mechanics in the two-dimensional torus without using position operators. We define an algebra with only momentum operators and shift operators and construct an irreducible representation of the algebra. We show that it realizes quantum mechanics of a charged particle in a uniform magnetic field and prove that any irreducible representation of the algebra is unitarily equivalent to each other. This work provides a firm foundation for the noncommutative torus theory.

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16

Campoamor-Stursberg, Rutwig, Hubert de Guise, and Marc de Montigny. "su(2) -expansion of the Lorentz algebra so(3,1 )." Canadian Journal of Physics 91, no. 8 (August 2013): 589–98. http://dx.doi.org/10.1139/cjp-2012-0391.

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We exploit the Iwasawa decomposition to construct coherent state representations of [Formula: see text], the Lorentz algebra in 3 + 1 dimensions, expanded on representations of the maximal compact subalgebra [Formula: see text]. Examples of matrix elements computation for finite dimensional and infinite-dimensional unitary representations are given. We also discuss different base vectors and the equivalence between these different choices. The use of the [Formula: see text]-matrix formalism to truncate the representation or to enforce unitarity is discussed.

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17

Paetznick, Adam, and Krysta M. Svore. "Repeat-Until-Success: Non-deterministic decomposition of single-qubit unitaries." Quantum Information and Computation 14, no. 15&16 (November 2014): 1277–301. http://dx.doi.org/10.26421/qic14.15-16-2.

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We present a decomposition technique that uses non-deterministic circuits to approximate an arbitrary single-qubit unitary to within distance $\epsilon$ and requires significantly fewer non-Clifford gates than existing techniques. We develop ``Repeat-Until-Success" (RUS) circuits and characterize unitaries that can be exactly represented as an RUS circuit. Our RUS circuits operate by conditioning on a given measurement outcome and using only a small number of non-Clifford gates and ancilla qubits. We construct an algorithm based on RUS circuits that approximates an arbitrary single-qubit $Z$-axis rotation to within distance $\epsilon$, where the number of $T$ gates scales as $1.26\log_2(1/\epsilon) - 3.53$, an improvement of roughly three-fold over state-of-the-art techniques. We then extend our algorithm and show that a scaling of $2.4\log_2(1/\epsilon) - 3.28$ can be achieved for arbitrary unitaries and a small range of $\epsilon$, which is roughly twice as good as optimal deterministic decomposition methods.

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18

JENKOVSZKY, LÁSZLÓ L., VOLODYMYR K. MAGAS, J. TIMOTHY LONDERGAN, and ADAM P. SZCZEPANIAK. "EXPLICIT MODEL REALIZING PARTON–HADRON DUALITY." International Journal of Modern Physics A 27, no. 26 (October 18, 2012): 1250157. http://dx.doi.org/10.1142/s0217751x12501576.

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We present a model that realizes both resonance-Regge (Veneziano) and parton–hadron (Bloom–Gilman) duality. We first review the features of the Veneziano model and we discuss how parton–hadron duality appears in the Bloom–Gilman model. Then we review limitations of the Veneziano model, namely that the zero-width resonances in the Veneziano model violate unitarity and Mandelstam analyticity. We discuss how such problems are alleviated in models that construct dual amplitudes with Mandelstam analyticity (so-called DAMA models). We then introduce a modified DAMA model, and we discuss its properties. We present a pedagogical model for dual amplitudes and we construct the nucleon structure function F2(x, Q2). We explicitly show that the resulting structure function realizes both Veneziano and Bloom–Gilman duality.

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19

BIRÓ, T. S. "CONSERVING ALGORITHMS FOR REAL-TIME NONABELIAN LATTICE GAUGE THEORIES." International Journal of Modern Physics C 06, no. 03 (June 1995): 327–44. http://dx.doi.org/10.1142/s0129183195000241.

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A class of numerical algorithms for solving the classical equations of motion in lattice gauge field theories which exactly fulfill the constraints imposed by the unitarity of the local group elements, by the local color charge conservation (Gauss law) and by the total energy conservation is constructed. The performance of these constrained algorithms is comparatively discussed.

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20

KIEU, T. D. "A FORMULATION OF CHIRAL GAUGE THEORIES OFF AND ON THE LATTICE." International Journal of Modern Physics A 07, no. 01 (January 10, 1992): 177–91. http://dx.doi.org/10.1142/s0217751x92000119.

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A formulation is proposed of Abelian chiral gauge theory which is invariant with respect to a gauge symmetry and admits both fermion and vector-boson mass terms, without invoking the Higgs mechanism. The issues of unitarity and renormalizability are discussed, and a lattice chiral regularization free from the problem of fermion-species doubling is constructed and compared with others.

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21

Sorensen, Danny C., and Yunkai Zhou. "Direct methods for matrix Sylvester and Lyapunov equations." Journal of Applied Mathematics 2003, no. 6 (2003): 277–303. http://dx.doi.org/10.1155/s1110757x03212055.

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We revisit the two standard dense methods for matrix Sylvester and Lyapunov equations: the Bartels-Stewart method forA1X+XA2+D=0and Hammarling's method forAX+XAT+BBT=0withAstable. We construct three schemes for solving the unitarily reduced quasitriangular systems. We also construct a new rank-1 updating scheme in Hammarling's method. This new scheme is able to accommodate aBwith more columns than rows as well as the usual case of aBwith more rows than columns, while Hammarling's original scheme needs to separate these two cases. We compared all of our schemes with the Matlab Sylvester and Lyapunov solverlyap.m; the results show that our schemes are much more efficient. We also compare our schemes with the Lyapunov solversllyapin the currently possibly the most efficient control library package SLICOT; numerical results show our scheme to be competitive.

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22

Montenegro, David, and B. M. Pimentel. "Planar generalized electrodynamics for one-loop amplitude in the Heisenberg picture." International Journal of Modern Physics A 36, no. 19 (July 5, 2021): 2150142. http://dx.doi.org/10.1142/s0217751x21501426.

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We examine the generalized quantum electrodynamics as a natural extension of the Maxwell electrodynamics to cure the one-loop divergence. We establish a precise scenario to discuss the underlying features between photon and fermion where the perturbative Maxwell electrodynamics fails. Our quantum model combines stability, unitarity, and gauge invariance as the central properties. To interpret the quantum fluctuations without suffering from the physical conflicts proved by Haag’s theorem, we construct the covariant quantization in the Heisenberg picture instead of the Interaction one. Furthermore, we discuss the absence of anomalous magnetic moment and mass-shell singularity.

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23

El Gradechi, Amine M. "On the Super-Unitarity of Discrete Series Representations of Orthosymplectic Lie Superalgebras." Reviews in Mathematical Physics 10, no. 04 (May 1998): 467–97. http://dx.doi.org/10.1142/s0129055x9800015x.

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We investigate the notion of super-unitarity from a functional analytic point of view. For this purpose we consider examples of explicit realizations of a certain type of irreducible representations of low rank orthosymplectic Lie superalgebras which are super-unitary by construction. These are the so-called superholomorphic discrete series representations of osp (1/2,ℝ) and osp (2/2,ℝ) which we recently constructed using a ℤ2–graded extension of the orbit method. It turns out here that super-unitarity of these representations is a consequence of the self-adjointness of two pairs of anticommuting operators which act in the Hilbert sum of two Hilbert spaces each of which carrying a holomorphic discrete series representation of su (1,1) such that the difference of the respective lowest weights is [Formula: see text]. At an intermediate stage, we show that the generators of the considered orthosymplectic Lie superalgebras can be realized either as matrix-valued first order differential operators or as first order differential superoperators. Even though the former realization is less convenient than the latter from the computational point of view, it has the advantage of avoiding the use of anticommuting Grassmann variables, and is moreover important for our analysis of super-unitarity. The latter emphasizes the fundamental role played by the atypical (or degenerate) superholomorphic discrete series representations of osp (2/2,ℝ) for the super-unitarity of the other representations considered in this work, and shows that the anticommuting (unbounded) self-adjoint operators mentioned above anticommute in a proper sense, thus connecting our work with the analysis of supersymmetric quantum mechanics.

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24

Stacey, P. J. "An Inductive Limit Model for the K-Theory of the Generator-Interchanging Antiautomorphism of an Irrational Rotation Algebra." Canadian Mathematical Bulletin 46, no. 3 (September 1, 2003): 441–56. http://dx.doi.org/10.4153/cmb-2003-044-0.

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AbstractLet Aθ be the universal C*-algebra generated by two unitaries U, V satisfying VU = e2πiθUV and let Φ be the antiautomorphism of Aθ interchanging U and V. The K-theory of Rθ = { a ∈ Aθ: Φ(a) = a*} is computed. When θ is irrational, an inductive limit of algebras of the form is constructed which has complexification Aθ and the same K-theory as Rθ.

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25

HÁJÍČEK, PETR, and CLAUS KIEFER. "SINGULARITY AVOIDANCE BY COLLAPSING SHELLS IN QUANTUM GRAVITY." International Journal of Modern Physics D 10, no. 06 (December 2001): 775–79. http://dx.doi.org/10.1142/s0218271801001578.

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We discuss a model describing exactly a thin spherically symmetric shell of matter with zero rest mass. We derive the reduced formulation of this system in which the variables are embeddings, their conjugate momenta, and Dirac observables. A nonperturbative quantum theory of this model is then constructed, leading to a unitary dynamics. As a consequence of unitarity, the classical singularity is fully avoided in the quantum theory.

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Brown, Lawrence G., and Hyun Ho Lee. "Homotopy Classification of Projections in the Corona Algebra of a Non-simple C*-algebra." Canadian Journal of Mathematics 64, no. 4 (August 1, 2012): 755–77. http://dx.doi.org/10.4153/cjm-2011-092-x.

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AbstractWe study projections in the corona algebra of C(X) ⊗ K, where K is the C*-algebra of compact operators on a separable infinite dimensional Hilbert space and X = [0, 1], [0,∞), (−∞,∞), or [0, 1]/﹛0, 1﹜. Using BDF's essential codimension, we determine conditions for a projection in the corona algebra to be liftable to a projection in the multiplier algebra. We also determine the conditions for two projections to be equal in K0, Murray-von Neumann equivalent, unitarily equivalent, or homotopic. In light of these characterizations, we construct examples showing that the equivalence notions above are all distinct.

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Lee, Cheng-Yang. "Symmetries and unitary interactions of mass dimension one fermionic dark matter." International Journal of Modern Physics A 31, no. 35 (December 18, 2016): 1650187. http://dx.doi.org/10.1142/s0217751x16501876.

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The fermionic fields constructed from Elko have several unexpected properties. They satisfy the Klein–Gordon but not the Dirac equation and are of mass dimension one instead of three-half. Starting with the Klein–Gordon Lagrangian, we initiate a careful study of the symmetries and interactions of these fermions and their higher-spin generalizations. We find, although the fermions are of mass dimension one, the four-point fermionic self-interaction violates unitarity at high-energy so it cannot be a fundamental interaction of the theory. Using the optical theorem, we derive an explicit bound on energy for the fermion–scalar interaction. It follows that for the spin-half fermions, the demand of renormalizability and unitarity forbids four-point interactions and only allows for the Yukawa interaction. For fermions with spin [Formula: see text], they have no renormalizable or unitary interactions. Since the theory is described by a Klein–Gordon Lagrangian, the interaction generated by the local [Formula: see text] gauge symmetry which contains a four-point interaction, is excluded by the demand of renormalizability. In the context of the Standard Model, these properties make the spin-half fermions natural dark matter candidates. Finally, we discuss the recent developments on the introduction of new adjoint and spinor duals which may allow us to circumvent the unitarity constraints on the interactions.

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LI, GUAN-NAN, HSIU-HSIEN LIN, DONG XU, and XIAO-GANG HE. "THE α, β AND γ PARAMETRIZATIONS OF CP-VIOLATING CKM PHASE." International Journal of Modern Physics A 28, no. 05n06 (March 10, 2013): 1350014. http://dx.doi.org/10.1142/s0217751x13500140.

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The CKM matrix describing quark mixing with three generations can be parametrized by three mixing angles and one CP-violating phase. In most of the parametrizations, the CP-violating phase chosen is not a directly measurable quantity and is parametrization dependent. In this work, we propose to use experimentally measurable CP-violating quantities, α, β or γ in the unitarity triangle as the phase in the CKM matrix, and construct explicit α, β and γ parametrizations. Approximate Wolfenstein-like expressions are also suggested. Since β is most accurately measured among these three phase angles, we consider β parametrization as the best one to use.

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RAVANINI, F. "ON THE POSSIBILITY OF ZN EXOTIC SUPERSYMMETRY IN TWO-DIMENSIONAL CONFORMAL FIELD THEORY." International Journal of Modern Physics A 07, no. 20 (August 10, 1992): 4949–63. http://dx.doi.org/10.1142/s0217751x92002246.

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We investigate the possibility to construct extended parafermionic conformal algebras whose generating current has spin [Formula: see text] generalizing the superconformal (spin 3/2) and the Fateev-Zamolodchikov (spin 4/3) algebras. Models invariant under such algebras would possess ZK exotic supersymmetries satisfying (supercharge)K=(momentum). However, we show that for K=4 this new algebra allows only for models at c=1, for K=5 it is a trivial rephrasing of the ordinary Z5 parafermionic model, for K=6, 7 (and, requiring unitarity, for all larger K) such algebras do not exist. Implications of this result for existence of exotic supersymmetry in two-dimensional field theory are discussed.

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FAIZAL, MIR. "ABSENCE OF BLACK HOLES INFORMATION PARADOX IN GROUP FIELD COSMOLOGY." International Journal of Geometric Methods in Modern Physics 11, no. 01 (December 16, 2013): 1450010. http://dx.doi.org/10.1142/s0219887814500108.

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In this paper we will analyze the black hole information paradox in group field cosmology. We will first construct a group field cosmology with third quantized gauge symmetry. Then we will argue that in this group field cosmology the process that changes the topology of spacetime is unitarity process. Thus, the information paradox from this perspective appears only because we are using a second quantized formalism to explain a third quantized process. A similar paradox would also occur if we analyze a second quantized process in first quantized formalism. Hence, we will demonstrate that in reality there is no information paradox but only a breakdown of the second quantized formalism.

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MIKOVIĆ, ALEKSANDAR. "CANONICAL QUANTIZATION APPROACH TO 2D GRAVITY COUPLED TO c < 1 MATTER." International Journal of Modern Physics A 09, no. 23 (September 20, 1994): 4195–210. http://dx.doi.org/10.1142/s0217751x94001710.

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We show that all important features of 2D gravity coupled to c < 1 matter can be easily understood from the canonical quantization approach à la Dirac. Furthermore, we construct a canonical transformation which maps the theory into a free field form, i.e. the constraints become free field Virasoro generators with background charges. This implies the gauge independence of the David–Distler–Kawai results, and also proves the free field assumption which was used for obtaining the spectrum of the theory in the conformal gauge. A discussion of the unitarity of the physical spectrum is presented and we point out that the scalar products of the discrete states are not well defined in the standard Fock space framework.

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Scholtz, F. G., P. H. Williams, and J. N. Kriel. "Commutative–non-commutative dualities." Canadian Journal of Physics 98, no. 2 (February 2020): 158–66. http://dx.doi.org/10.1139/cjp-2018-0887.

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We show that it is in principle possible to construct dualities between commutative and non-commutative theories in a systematic way. This construction exploits a generalization of the exact renormalization group equation (ERG). We apply this to the simple case of the Landau problem and then generalize it to the free and interacting non-canonical scalar field theory. This constructive approach offers the advantage of tracking the implementation of the Lorentz symmetry in the non-commutative dual theory. In principle, it allows for the construction of completely consistent non-commutative and non-local theories where the Lorentz symmetry and unitarity are still respected, but may be implemented in a highly non-trivial and non-local manner.

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KROMMWEH, JENS. "TIGHT FRAME CHARACTERIZATION OF MULTIWAVELET VECTOR FUNCTIONS IN TERMS OF THE POLYPHASE MATRIX." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 01 (January 2009): 9–21. http://dx.doi.org/10.1142/s0219691309002751.

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The extension principles play an important role in characterizing and constructing of wavelet frames. The common extension principles, the unitary extension principle (UEP) or the oblique extension principle (OEP), are based on the unitarity of the modulation matrix. In this paper, we state the UEP and OEP for refinable function vectors in the polyphase representation. Finally, we apply our results to directional wavelets on triangles which we have constructed in a previous work. We will show that the wavelet system generates a tight frame for L2(ℝ2).

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Traubenberg, M. Rausch de, and M. J. Slupinski. "Nontrivial Extensions of the 3D-Poincaré Algebra and Fractional Supersymmetry for Anyons." Modern Physics Letters A 12, no. 39 (December 21, 1997): 3051–66. http://dx.doi.org/10.1142/s0217732397003174.

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Nontrivial extensions of three-dimensional Poincaré algebra, beyond the supersymmetric one, are explicitly constructed. These algebraic structures are the natural three-dimensional generalizations of fractional supersymmetry of order F already considered in one and two dimensions. Representations of these algebras are exhibited, and unitarity is explicitly checked. It is then shown that these extensions generate symmetries which connect fractional spin states or anyons. Finally, a natural classification arises according to the decomposition of F into its product of prime numbers leading to subsystems with smaller symmetries.

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Avila, Ricardo, and Carlos M. Reyes. "Optical theorem and indefinite metric in λϕ4 delta-theory." International Journal of Modern Physics A 35, no. 33 (November 20, 2020): 2050214. http://dx.doi.org/10.1142/s0217751x20502140.

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A class of effective field theory called delta-theory, which improves ultraviolet divergences in quantum field theory, is considered. We focus on a scalar model with a quartic self-interaction term and construct the delta theory by applying the so-called delta prescription. We quantize the theory using field variables that diagonalize the Lagrangian, which include a standard scalar field and a ghost or negative norm state. As well known, the indefinite metric may lead to the loss of unitary of the [Formula: see text]-matrix. We study the optical theorem and check the validity of the cutting equations for three processes at one-loop order, and found suppressed violations of unitarity in the delta coupling parameter of the order of [Formula: see text].

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ARNONE, STEFANO, YURI A. KUBYSHIN, TIM R. MORRIS, and JOHN F. TIGHE. "GAUGE-INVARIANT REGULARISATION VIA SU(N|N)." International Journal of Modern Physics A 17, no. 17 (July 10, 2002): 2283–329. http://dx.doi.org/10.1142/s0217751x02009722.

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We construct a gauge-invariant regularisation scheme for pure SU(N) Yang–Mills theory in dimension four or less (for N = ∞ in all dimensions), with a physical cutoff scale Λ, by using covariant higher derivatives and spontaneously broken SU(N|N) supergauge invariance. Providing their powers are within certain ranges, the covariant higher derivatives cure the superficial divergence of all but a set of one-loop graphs. The finiteness of these latter graphs is ensured by properties of the supergroup and gauge invariance. In the limit Λ → ∞, all the regulator fields decouple and unitarity is recovered in the renormalized pure SU(N) Yang–Mills theory. By demonstrating these properties, we prove that the regularisation works to all orders in perturbation theory.

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37

ELSAEV, Yakub V. "On a dilation of a some class of completely positive maps." Tambov University Reports. Series: Natural and Technical Sciences, no. 127 (2019): 333–39. http://dx.doi.org/10.20310/2686-9667-2019-24-127-333-339.

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In this article we investigate sesquilinear forms defined on the Cartesian product of Hilbert C^*-module M over C^*-algebra B and taking values in B. The set of all such defined sesquilinear forms is denoted by S_B (M). We consider completely positive maps from locally C^*-algebra A to S_B (M). Moreover we assume that these completely positive maps are covariant with respect to actions of a group symmetry. This allow us to view these maps as generalizations covariant quantum instruments which are very important for the modern quantum mechanic and the quantum field theory. We analyze the dilation problem for these class of maps. In order to solve this problem we construct the minimal Stinespring representation and prove that every two minimal representations are unitarily equivalent.

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VASSELLI, EZIO. "CROSSED PRODUCTS BY ENDOMORPHISMS, VECTOR BUNDLES AND GROUP DUALITY." International Journal of Mathematics 16, no. 02 (February 2005): 137–71. http://dx.doi.org/10.1142/s0129167x05002783.

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We construct the crossed product [Formula: see text] of a C(X)-algebra [Formula: see text] by an endomorphism ρ, in such a way that ρ becomes induced by the bimodule [Formula: see text] of continuous sections of a vector bundle ℰ → X. Some motivating examples for such a construction are given. Furthermore, we study the C*-algebra of G-invariant elements of the Cuntz-Pimsner algebra [Formula: see text] associated with [Formula: see text], where G is a (noncompact, in general) group acting on ℰ. In particular, the C*-algebra of invariant elements with respect to the action of the group of special unitaries of ℰ is a crossed product in the above sense. We also study the analogous construction on certain Hilbert bimodules, called "noncommutative pullbacks".

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39

Buoninfante, Luca, Gaetano Lambiase, and Masahide Yamaguchi. "Enlarging local symmetries: A nonlocal Galilean model." International Journal of Geometric Methods in Modern Physics 17, supp01 (May 26, 2020): 2040009. http://dx.doi.org/10.1142/s0219887820400095.

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We consider the possibility to enlarge the class of symmetries realized in standard local field theories by introducing infinite order derivative operators in the actions, which become nonlocal. In particular, we focus on the Galilean shift symmetry and its generalization in nonlocal (infinite derivative) field theories. First, we construct a nonlocal Galilean model which may be UV finite, showing how the ultraviolet behavior of loop integrals can be ameliorated. We also discuss the pole structure of the propagator which has infinitely many complex conjugate poles, but satisfies tree level unitarity. Moreover, we will introduce the same kind of nonlocal operators in the context of linearized gravity. In such a scenario, the graviton propagator turns out to be ghost-free and the spacetime metric generated by a point-like source is non-singular.

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Kieburg, Mario, and Holger Kösters. "Exact relation between singular value and eigenvalue statistics." Random Matrices: Theory and Applications 05, no. 04 (October 2016): 1650015. http://dx.doi.org/10.1142/s2010326316500155.

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We use classical results from harmonic analysis on matrix spaces to investigate the relation between the joint densities of the singular values and the eigenvalues for complex random matrices which are bi-unitarily invariant (also known as isotropic or unitary rotation invariant). We prove that each of these joint densities determines the other one. Moreover, we construct an explicit formula relating both joint densities at finite matrix dimension. This relation covers probability densities as well as signed densities. With the help of this relation we derive general analytical relations among the corresponding kernels and biorthogonal functions for a specific class of polynomial ensembles. Furthermore, we show how to generalize the relation between the singular value and eigenvalue statistics to certain situations when the ensemble is deformed by a term which breaks the bi-unitary invariance.

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Singh, Ajit. "Role Of Partial Transpose And Generalized Choi Maps In Quantum Dynamical Semigroups Involving Separable And Entangled States." Electronic Journal of Linear Algebra 29 (September 20, 2015): 156–93. http://dx.doi.org/10.13001/1081-3810.2975.

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Power symmetric stochastic matrices introduced by R. Sinkhorn (1981) and their generalization by R.B. Bapat, S.K. Jain and K. Manjunatha Prasad (1999) have been utilized to give positive block matrices with trace one possessing positive partial transpose, the so-called PPT states. Another method to construct such PPT states is given, it uses the form of a matrix unitarily equivalent to to its transpose obtained by S.R. Garcia and J.E. Tener (2012). Evolvement or suppression of separability or entanglement of various levels for a quantum dynamical semigroup of completely positive maps has been studied using Choi-Jamiolkowsky matrix of such maps and the famous Hordeckis criteria (1996). A Trichotomy Theorem has been proved, and examples have been given that depend mainly on generalized Choi maps and clearly distinguish the levels of entanglement breaking.

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42

Nakatsugawa, Keiji, Motoo Ohaga, Toshiyuki Fujii, Toyoki Matsuyama, and Satoshi Tanda. "The Nakano–Nishijima–Gell-Mann Formula from Discrete Galois Fields." Symmetry 12, no. 10 (September 26, 2020): 1603. http://dx.doi.org/10.3390/sym12101603.

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The well known Nakano–Nishijima–Gell-Mann (NNG) formula relates certain quantum numbers of elementary particles to their charge number. This equation, which phenomenologically introduces the quantum numbers Iz (isospin), S (strangeness), etc., is constructed using group theory with real numbers R. But, using a discrete Galois field Fp instead of R and assuring the fundamental invariance laws such as unitarity, Lorentz invariance, and gauge invariance, we derive the NNG formula deductively from Meson (two quarks) and Baryon (three quarks) representations in a unified way. Moreover, we show that quark confinement ascribes to the inevitable fractionality caused by coprimeness between half-integer (1/2) of isospin and number of composite particles (e.g., three).

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MOHAPATRA, A. K. "A HIGH-PT TRIGGER FOR THE HERA-B EXPERIMENT." International Journal of Modern Physics A 16, supp01c (September 2001): 1156–58. http://dx.doi.org/10.1142/s0217751x01009181.

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We have constructed a high-pT trigger for the HERA-B experiment at DESY. The HERA-B experiment produces B mesons by inserting wire targets into the halo of the proton beam circulating in HERA. The high-pt trigger records events that contain tracks that have high transverse momentum with respect to the beam. Such a trigger is efficient for recording B → π+π-, B → K- π+, Bs → K+ K-, [Formula: see text], and other topical hadronic B decays. These decays provide sensitivity to the internal angles alpha and gamma of the CKM unitarity triangle, and they also can be used to measure or constrain the [Formula: see text] mixing parameter xs.

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44

Haller, Kurt, and Edwin Lim-Lombridas. "Gauss's Law, Gauge-Invariant States, and Spin & Statistics in Abelian Chern-Simons Theories." International Journal of Modern Physics A 12, no. 06 (March 10, 1997): 1053–62. http://dx.doi.org/10.1142/s0217751x97000785.

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We discuss topologically massive QED — the Abelian gauge theory in which (2+1)-dimensional QED with a Chern-Simons term is minimally coupled to a spinor field. We quantize the theory in covariant gauges, and construct a class of unitary transformations that enable us to embed the theory in a Fock space of states that implement Gauss's law. We show that when electron (and positron) creation and annihilation operators represent gauge-invariant charged particles that are surrounded by the electric and magnetic fields required by Gauss's law, the unitarity of the theory is manifest, and charged particles interact with photons and with each other through nonlocal potentials. These potentials include a Hopf-like interaction, and a planar analog of the Coulomb interaction. The gauge-invariant charged particle excitations that implement Gauss's law obey the identical anticommutation rules as do the original gauge-dependent ones. Rotational phases, commonly identified as planar 'spin' are arbitrary, however.

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ISOZAKI, HIROSHI. "QFT FOR SCALAR PARTICLES IN EXTERNAL FIELDS ON RIEMANNIAN MANIFOLDS." Reviews in Mathematical Physics 13, no. 06 (June 2001): 767–98. http://dx.doi.org/10.1142/s0129055x01000831.

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We introduce a class of noncompact Riemannian manifolds on which we can argue quantum field theory for scalar particles in external fields. More precisely, we consider quantized linear Klein–Gordon fields subject to (non quantized) electromagnetic forces in a certain class of static space-time. This class is broad enough to include physically important examples of the Euclidean space, the hyperbolic space, and by passing to the natural Lorentzian structure, the Schwarzschild metric up to conformal equivalence. The S-matrix of the massive Klein–Gordon equation on these manifolds is unitarily implemented on the Fock space constructed via the spectrum of the Laplace–Beltrami operator with scalar curvature. We also give the same result for the massless case in the asymptotically flat and hyperbolic spaces.

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46

Bergshoeff, Eric, Wout Merbis, Alasdair J. Routh, and Paul K. Townsend. "The third way to 3D gravity." International Journal of Modern Physics D 24, no. 12 (October 2015): 1544015. http://dx.doi.org/10.1142/s0218271815440150.

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Consistency of Einstein’s gravitational field equation [Formula: see text] imposes a “conservation condition” on the [Formula: see text]-tensor that is satisfied by (i) matter stress tensors, as a consequence of the matter equations of motion and (ii) identically by certain other tensors, such as the metric tensor. However, there is a third way, overlooked until now because it implies a “nongeometrical” action: one not constructed from the metric and its derivatives alone. The new possibility is exemplified by the 3D “minimal massive gravity” model, which resolves the “bulk versus boundary” unitarity problem of topologically massive gravity with Anti-de Sitter asymptotics. Although all known examples of the third way are in three spacetime dimensions, the idea is general and could, in principle, apply to higher dimensional theories.

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47

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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48

Sepehri, Alireza, Somayyeh Shoorvazi, and Mohammad Ebrahim Zomorrodian. "Does the HM mechanism work in string theory?" Canadian Journal of Physics 91, no. 1 (January 2013): 75–80. http://dx.doi.org/10.1139/cjp-2012-0163.

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The correspondence principle offers a unique opportunity to test the Horowitz and Maldacena mechanism at the correspondence point “the centre of mass energies around (Ms/(gs)2)”. First by using the Horowitz and Maldacena proposal, the black hole final state for closed strings is studied and the entropy of these states is calculated. Then, to consider the closed string states, a copy of the original Hilbert space is constructed with a set of creation–annihilation operators that have the same commutation properties as the original ones. The total Hilbert space is the tensor product of the two spaces Hright ⊗ Hleft, where in this case Hleft/right denote the physical quantum state space of the closed string. It is shown that closed string states can be represented by a maximally entangled two-mode squeezed state of the left and right spaces of closed string. Also, the entropy for these string states is calculated. It is found that black hole entropy matches the closed string entropy at transition point. This means that our result is consistent with correspondence principle and thus HM mechanism in string theory works. Consequently the unitarity of the black hole in string theory can be reconciled. However Gottesman and Preskill point out that, in this scenario, departures from unitarity can arise due to interactions between the collapsing body and the infalling Hawking radiation inside the event horizon and information can be lost. By extending the Gottesman and Preskill method to string theory, the amount of information transformation from the matter to the state of outgoing Hagedorn radiation for closed strings is obtained. It is observed that information is lost for closed strings.

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Contogouris, A. P., N. Mebarki, and D. Atwood. "DISPERSION RELATIONS APPROACH FOR HEAVY HIGGS." International Journal of Modern Physics A 02, no. 04 (August 1987): 1075–83. http://dx.doi.org/10.1142/s0217751x87000478.

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The system of interacting Higgs and longitudinal gauge bosons, when the Higgs mass MH varies above 1 TeV, is studied using dispersion relations (N/D method). Models satisfying unitarity and analyticity constraints are constructed and solved exactly. For MH≲0.6 TeV the dispersive and perturbative (tree level) amplitudes are similar. For MH≳1.5 TeV , however, they much differ in structure. For MH≃1.5, in ZZ→ZZ the dispersive amplitudes exceed the perturbative ones by factors 2~4. There are indications of strong interaction effects: In HH→HH there is an ℓ=0 bound state, which can be taken as the Higgs itself; in fact, for MH≃2.5 there is an almost self-consistent solution with respect to the mass, and very roughly with respect to the coupling. There is also some indication of a resonance in ZZ→ZZ, as well as in HH→HH.

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Mannheim, Philip D. "PT symmetry as a necessary and sufficient condition for unitary time evolution." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1989 (April 28, 2013): 20120060. http://dx.doi.org/10.1098/rsta.2012.0060.

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While Hermiticity of a time-independent Hamiltonian leads to unitary time evolution, in and of itself, the requirement of Hermiticity is only sufficient for unitary time evolution. In this paper, we provide conditions that are both necessary and sufficient. We show that symmetry of a time-independent Hamiltonian, or equivalently, reality of the secular equation that determines its eigenvalues, is both necessary and sufficient for unitary time evolution. For any -symmetric Hamiltonian H , there always exists an operator V that relates H to its Hermitian adjoint according to V HV −1 = H † . When the energy spectrum of H is complete, Hilbert space norms 〈 ψ 1 | V | ψ 2 〉 constructed with this V are always preserved in time. With the energy eigenvalues of a real secular equation being either real or appearing in complex conjugate pairs, we thus establish the unitarity of time evolution in both cases. We also establish the unitarity of time evolution for Hamiltonians whose energy spectra are not complete. We show that when the energy eigenvalues of a Hamiltonian are real and complete, the operator V is a positive Hermitian operator, which has an associated square root operator that can be used to bring the Hamiltonian to a Hermitian form. We show that systems with -symmetric Hamiltonians obey causality. We note that Hermitian theories are ordinarily associated with a path integral quantization prescription in which the path integral measure is real, while in contrast, non-Hermitian but -symmetric theories are ordinarily associated with path integrals in which the measure needs to be complex, but in which the Euclidean time continuation of the path integral is nonetheless real. Just as the second-order Klein–Gordon theory is stabilized against transitions to negative frequencies because its Hamiltonian is positive-definite, through symmetry, the fourth-order derivative Pais–Uhlenbeck theory can equally be stabilized.

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