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Journal articles on the topic 'Bose-Algebra'

Author: Grafiati

Published: 4 June 2021

Last updated: 29 January 2023

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1

Ikuta, Takuya, and Akihiro Munemasa. "Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4." Special Matrices 6, no. 1 (January 1, 2018): 1–10. http://dx.doi.org/10.1515/spma-2018-0001.

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Abstract We consider nonsymmetric hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of commutative nonsymmetric association schemes. First, we give a characterization of the eigenmatrix of a commutative nonsymmetric association scheme of class 3 whose Bose-Mesner algebra contains a nonsymmetric hermitian complex Hadamard matrix, and show that such a complex Hadamard matrix is necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.We also give nonsymmetric association schemes X of class 6 on Galois rings of characteristic 4, and classify hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of X. It is shown that such a matrix is again necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.

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2

Steeb, W. H. "Bose-Fermi systems and computer algebra." Foundations of Physics Letters 8, no. 1 (February 1995): 73–81. http://dx.doi.org/10.1007/bf02187533.

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3

SCIPIONI, R. "G-ALGEBRA AND CURVED SPACETIME." Modern Physics Letters A 10, no. 23 (July 30, 1995): 1705–9. http://dx.doi.org/10.1142/s0217732395001824.

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The recently proved nonexistence of generalized statistics in curved spacetime is reconsidered in the framework of g-algebra; we show in a rigorous way that for asymptotic states, a Fermi or Bose statistics in the “in” region always evolves a Bose or Fermi statistics in the “out” region; the new approach, however, permits one to infer that this fact might not be true when considering intermediate states.

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4

HOSSEINI, A., and A. RAHNAMAI BARGHI. "TABLE ALGEBRAS OF RANK 3 AND ITS APPLICATIONS TO STRONGLY REGULAR GRAPHS." Journal of Algebra and Its Applications 12, no. 05 (May 7, 2013): 1250216. http://dx.doi.org/10.1142/s0219498812502167.

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A table algebra is called quasi self-dual if there exists a permutation on the set of primitive idempotents under which any Krein parameter is equal to its corresponding structure constants. In this paper we investigate the question of when a table algebra of rank 3 is quasi self-dual. As a direct consequence we find necessary and sufficient conditions for the Bose–Mesner algebra of a given strongly regular graph to be quasi self-dual. In fact, our result generalizes the well-known Delsarte's characterization of a self-duality of the Bose–Mesner algebra of a strongly regular graph given in [P. Delsarte, An algebraic approach to the association schemes of coding theory, Philips Res. Rep. Suppl.10 (1973) 1–97]. Among our results we determine conditions under which the Krein parameters of an integral table algebra of rank 3 are non-negative rational numbers.

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5

SHANTA, P., S. CHATURVEDI, A. K. KAPOOR, and V. SRINIVASAN. "PARASTATISTICAL SYSTEMS AT FINITE TEMPERATURES IN THERMOFIELD DYNAMICS." International Journal of Modern Physics A 07, no. 16 (June 30, 1992): 3807–16. http://dx.doi.org/10.1142/s0217751x92001691.

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We consider para-Bose and para-Fermi oscillators within the framework of thermofield dynamics. For these systems, we construct the transformation relating the thermal vacuum state to the zero temperature vacuum. This construction makes use of a nonlinear realization of the single mode para-Bose (para-Fermi) algebra in terms of a single boson.

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6

Hamid, Nur, Cahyu Guswita, Saiful Islam, and M. Faiz Nailun Ni'am. "IDEMPOTEN PRIMITIF SKEMA ASOSIASI GRUP UNTUK MATRIKS GRUP ATAS Z_3." Jurnal Kajian Matematika dan Aplikasinya (JKMA) 2, no. 2 (June 11, 2021): 21. http://dx.doi.org/10.17977/um055v2i22021p21-25.

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Some combinatorial problems in Mathematics can be studied via association scheme. By this scheme, algebra structure called Bose-Mesner algebra can be obtained. In this article, we show the explicit forms of the idempotent primitive of an association scheme for the group of order 48. Keywords: Association scheme, idempotent primitif

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7

Brodimas, G., A. Jannussis, and R. Mignani. "Bose realization of a non-canonical Heisenberg algebra." Journal of Physics A: Mathematical and General 25, no. 7 (April 7, 1992): L329—L334. http://dx.doi.org/10.1088/0305-4470/25/7/008.

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8

CELEGHINI, ENRICO. "A NEW DEFINITION OF BOSONS." International Journal of Modern Physics B 13, no. 24n25 (October 10, 1999): 2909–13. http://dx.doi.org/10.1142/s0217979299002733.

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A recipe is given to reproduce algebraically the Bose prescription in Quantum Statistics. Bosons are thus defined as coherent states of the [Formula: see text] representation of the Lie-Hopf algebra su(1, 1), while h(1) is shown to be related to Boltzmann statistics. The technical power of group theory is used to show that black-body radiation formula as well as all other experimental results obtained in continuum limit do not require Bose distribution but are compatible with many other less symmetric ones. This may have dramatical effects on the predictions on Bose condensation.

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9

AMICO, LUIGI. "ALGEBRAIC EQUIVALENCE BETWEEN CERTAIN MODELS FOR SUPERFLUID–INSULATOR TRANSITION." Modern Physics Letters B 14, no. 21 (September 10, 2000): 759–66. http://dx.doi.org/10.1142/s0217984900000963.

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Algebraic contraction is proposed to realize mappings between Hamiltonian models. This transformation contracts the algebra of the degrees of freedom underlying the Hamiltonian. The rigorous mapping between the anisotropic XXZ Heisenberg model, the quantum phase model and the Bose Hubbard model is established as the contractions of the algebra u(2) underlying the dynamics of the XXZ Heisenberg model.

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10

Maule, Milena, and Stefano Sciuto. "Extended Conformal Symmetry of the One-Dimensional Bose Gas." Modern Physics Letters A 12, no. 29 (September 21, 1997): 2153–59. http://dx.doi.org/10.1142/s021773239700220x.

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We show that the low-lying excitations of the one-dimensional Bose gas are described, at all orders in a 1/N expansion and at the first order in the inverse of the coupling constant, by an effective Hamiltonian written in terms of an extended conformal algebra, namely the Cartan subalgebra of the [Formula: see text] algebra. This enables us to construct the first interaction term which corrects the Hamiltonian of the free fermions equivalent to a hard-core boson system.

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11

R-MONTEIRO, M., and L. M. C. S. RODRIGUES. "INEQUIVALENT REPRESENTATIONS OF A q-OSCILLATOR ALGEBRA IN A QUANTUM q-GAS." Modern Physics Letters B 09, no. 14 (June 20, 1995): 883–87. http://dx.doi.org/10.1142/s021798499500084x.

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We study the consequences of inequivalent representations of a q-oscillator algebra on a quantum q-gas. As in the "fundamental" representation of the algebra, the q-gas presents the Bose-Einstein condensation phenomenon and a λ-point transition. The virial expansion and the critical temperature of condensation are very sensible to the representation chosen; instead, the discontinuity in the λ-point transition is unaffected.

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12

Huang, Zhiyuan, and Shunlong Luo. "Wick Calculus of Generalized Operators and its Applications to Quantum Stochastic Calculus." Infinite Dimensional Analysis, Quantum Probability and Related Topics 01, no. 03 (July 1998): 455–66. http://dx.doi.org/10.1142/s0219025798000247.

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A nonlinear and stochastic analysis of free Bose field is established in the framework of white noise calculus. Wick algebra structure is introduced in the space of generalized operators generated by quantum white noise, some fundamental properties of the calculus based on the Wick algebra are investigated. As applications, quantum stochastic integrals and quantum stochastic differential equations are treated from the viewpoint of Wick calculus.

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13

Vakarchuk, I. O., and G. Panochko. "The Effective Mass of an Impurity Atom in the Bose Liquid with a Deformed Heisenberg Algebra." Ukrainian Journal of Physics 62, no. 2 (February 2017): 123–31. http://dx.doi.org/10.15407/ujpe62.02.0123.

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14

Jensen, Ole Rask, and Erik Bjerrum Nielsen. "A Bose-Fock space quantization of the Witt algebra." Reports on Mathematical Physics 37, no. 2 (April 1996): 157–61. http://dx.doi.org/10.1016/0034-4877(96)89761-8.

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15

STEEB, WILLI-HANS, and YORICK HARDY. "QUANTUM OPTICS NETWORKS, UNITARY OPERATORS AND COMPUTER ALGEBRA." International Journal of Modern Physics C 19, no. 07 (July 2008): 1069–78. http://dx.doi.org/10.1142/s0129183108012674.

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In linear quantum optics we consider phase shifters, beam splitters, displacement operations, squeezing operations etc. The evolution can be described by unitary operators using Bose creation and annihilation operators. This evolution can be reduced to matrix multiplication using unitary matrices. We derive these evolutions for the different unitary operators. Finally a computer algebra implementation is provided.

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16

Huang, Xun, Xu-Yang Hou, Yan Gong, and Hao Guo. "Finite temperature behaviors of q-deformed Fermi gases." Modern Physics Letters B 33, no. 24 (August 30, 2019): 1950294. http://dx.doi.org/10.1142/s0217984919502944.

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During the last three decades, nonstandard statistics for indistinguishable quantum particles has attracted wide attention and research interests from many institutions. Among these new types of statistics, the [Formula: see text]-deformed Bose and Fermi statistics, originated from the study of quantum algebra, are being applied in more and more physical systems. In this paper, we construct a [Formula: see text]-deformed generalization of the BCS-Leggett theory for ultracold Fermi gases based on our previously constructed [Formula: see text]-deformed BCS theory. Some interesting features of this [Formula: see text]-deformed interacting quantum gas are obtained by numerical analysis. For example, in the ordinary Bose–Einstein Condensation regime, the gas presents a fermionic feature instead of bosonic feature if the deformation parameter is tuned suitably, which might be referred to as the [Formula: see text]-induced “Bose–Fermi” crossover. Conversely, a weak sign of the “Fermi–Bose” crossover is also found in the ordinary weak fermionic regime.

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17

Chubai, O. M., and A. A. Rovenchak. "Ideal Bose Gas in Some Deformed Types of Thermodynamics. Correspondence between Deformation Parameters." Ukrainian Journal of Physics 65, no. 6 (June 9, 2020): 500. http://dx.doi.org/10.15407/ujpe65.6.500.

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Two approaches to the construction of thermodynamics in the framework of the q- and м-formalisms, which correspond to certain deformations of the algebra of the creation–annihilation operators, have been considered. By comparing the obtained results, an approximate, independent of the space dimension, correspondence was revealed between the second virial coefficients for the ideal q- and м-deformed Bose gases. The corresponding discrepancy arises only at the level of the third virial coefficient. A method for emulating the м-deformed Bose gas up to the third virial coefficient inclusive by means of the two-parametric nonadditive Polychronakos statistics is demonstrated.

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18

RUSSO, JORGE. "BOSONIZATION AND FERMION VERTICES ON AN ARBITRARY GENUS RIEMANN SURFACE BY USING A GLOBAL OPERATOR FORMALISM." Modern Physics Letters A 04, no. 24 (November 20, 1989): 2349–62. http://dx.doi.org/10.1142/s0217732389002641.

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Fermi-Bose equivalence is studied with the use of a global operator formalism on Riemann surfaces of arbitrary topology. The quantization of a scalar field on a circle is performed in detail, globally, at arbitrary genus. A new algebra of the Krichever-Novikov type naturally emerges. This admits three central extensions and generalizes standard algebras of the sphere to higher genus. It is shown by explicit computation that the central terms, as well as correlation functions, corresponding to the Bose and Fermi models agree. Spin fields and fermion vertices are defined within this framework and their conformal properties are investigated.

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19

FRANZOSI, ROBERTO, VITTORIO PENNA, and RICCARDO ZECCHINA. "QUANTUM DYNAMICS OF COUPLED BOSONIC WELLS WITHIN THE BOSE–HUBBARD PICTURE." International Journal of Modern Physics B 14, no. 09 (April 10, 2000): 943–61. http://dx.doi.org/10.1142/s0217979200001011.

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We relate the quantum dynamics of the Bose–Hubbard model (BHM) to the semiclassical nonlinear equations that describe an array of interacting Bose condensates by implementing a standard variational procedure based on the coherent state method. We investigate the dynamics of the two-site BHM from the purely quantum viewpoint by recasting first the model within a spin picture and using then the related dynamical algebra. The latter allows us to study thoroughly the energy spectrum structure and to interpret quantally the classical symmetries of the two-site dynamics. The energy spectrum is also evaluated through various approximations relying on the coherent state approach.

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20

NARAYANA SWAMY, P. "INTERPOLATING STATISTICS AND q-DEFORMED OSCILLATOR ALGEBRAS." International Journal of Modern Physics B 20, no. 06 (March 10, 2006): 697–713. http://dx.doi.org/10.1142/s0217979206033498.

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The idea that a system obeying interpolating statistics can be described by a deformed oscillator algebra, or quantum groups, has been an outstanding issue. We are able to demonstrate that a q-deformed oscillator algebra can be used to describe the statistics of particles which provide a continuous interpolation between Bose and Fermi statistics. We show that the generalized intermediate statistics splits into Boson-like and Fermion-like regimes, each described by a unique oscillator algebra. The thermostatistics of Boson-like particles is described by employing q-calculus based on the Jackson derivative while the Fermion-like particles are described by ordinary derivatives of thermodynamics. Thermodynamic functions for systems of both types are determined and examined.

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21

JING, SICONG, and CHARLES A. NELSON. "DIRAC'S CONTOUR REPRESENTATION FOR PARAPARTICLES." Modern Physics Letters A 13, no. 34 (November 10, 1998): 2779–88. http://dx.doi.org/10.1142/s0217732398002953.

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Dirac's contour representation is extended to para-Bose and para-Fermi systems by use of deformed algebra techniques. In this analytic representation, the action of the para-particle annihilation operator is equivalent to a deformed differentiation which encodes the statistics of the paraparticle. In the para-Fermi case, the derivative's ket-domain is degree p polynomial.

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22

FAN, HONG-YI, and SHU-GUANG LIU. "NEW n-MODE BOSE OPERATOR REALIZATION OF SU(2) LIE ALGEBRA AND ITS APPLICATION IN ENTANGLED FRACTIONAL FOURIER TRANSFORM." Modern Physics Letters A 24, no. 08 (March 14, 2009): 615–24. http://dx.doi.org/10.1142/s0217732309027418.

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We introduce a new n-mode Bose operator realization of SU(2) Lie algebra and link it to the two mutually conjugate multipartite entangled state representations. In so doing we are naturally lead to the n-mode entangle fractional Fourier transform (EFFT), which provides us with a convenient way to deriving the EFFT of quantum-mechanical wave functions.

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23

SKEIDE, MICHAEL. "A CENTRAL LIMIT THEOREM FOR BOSE ${\mathcal Z}$-INDEPENDENT QUANTUM RANDOM VARIABLES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 02, no. 02 (June 1999): 289–99. http://dx.doi.org/10.1142/s0219025799000163.

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We present a central limit theorem for Bose [Formula: see text]-independent operator-valued random variables. Furthermore, we show that the central limit distribution may be represented by an algebra of creators and annihilators on a symmetric Fock module. As an example we recover the distribution of creators and annihilators on the truncated Fock space, i.e. the central limit distribution of Boolean independence.

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24

Randriamaro, Hery. "A Deformed Quon Algebra." Communications in Mathematics 27, no. 2 (December 1, 2019): 103–12. http://dx.doi.org/10.2478/cm-2019-0010.

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AbstractThe quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and creation operators obey the quon algebra which interpolates between fermions and bosons. In this paper we generalize these models by introducing a deformation of the quon algebra generated by a collection of operators ai,k, (i, k) ∈ ℕ* × [m], on an infinite dimensional vector space satisfying the deformed q-mutator relations {a_j}_{,l}a_{i,k}^\dagger = qa_{i,k}^\dagger{a_{j,l}} + {q^{{\beta _{k,l}}}}{\delta _{i,j}} We prove the realizability of our model by showing that, for suitable values of q, the vector space generated by the particle states obtained by applying combinations of ai,k’s and a_{i,k}^\dagger ‘s to a vacuum state |0〉 is a Hilbert space. The proof particularly needs the investigation of the new statistic cinv and representations of the colored permutation group.

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25

MELJANAC, STJEPAN, and MARIJAN MILEKOVIĆ. "A UNIFIED VIEW OF MULTIMODE ALGEBRAS WITH FOCK-LIKE REPRESENTATIONS." International Journal of Modern Physics A 11, no. 08 (March 30, 1996): 1391–412. http://dx.doi.org/10.1142/s0217751x9600064x.

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A unified view of general multimode oscillator algebras with Fock-like representations is presented. It extends a previous analysis of the single-mode oscillator algebras. The expansion of the [Formula: see text] operators is extended to include all normally ordered terms in creation and annihilation operators, and we analyze their action on Fock-like states. We restrict ourselves to the algebras compatible with number operators. The connection between these algebras and generalized statistics is analyzed. We demonstrate our approach by considering the algebras obtainable from the generalized Jordan-Wigner transformation, the para-Bose and para-Fermi algebras, the Govorkov “paraquantization” algebra and generalized quon algebra.

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26

Eisfeld, Jörg. "Subsets of association schemes corresponding to eigenvectors of the Bose-Mesner algebra." Bulletin of the Belgian Mathematical Society - Simon Stevin 5, no. 2/3 (1998): 265–74. http://dx.doi.org/10.36045/bbms/1103409010.

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27

Takeyama, Yoshihiro. "A Discrete Analogue of Periodic Delta Bose Gas and Affine Hecke Algebra." Funkcialaj Ekvacioj 57, no. 1 (2014): 107–18. http://dx.doi.org/10.1619/fesi.57.107.

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28

Jafarizadeh, M. A., S. Behnia, E. Faizi, and S. Ahadpour. "Generalized N-coupled maps with invariant measure in Bose-Mesner algebra perspective." Pramana 70, no. 3 (March 2008): 417–38. http://dx.doi.org/10.1007/s12043-008-0059-3.

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29

Buchholz, Detlev. "The Resolvent Algebra of Non-relativistic Bose Fields: Observables, Dynamics and States." Communications in Mathematical Physics 362, no. 3 (May 15, 2018): 949–81. http://dx.doi.org/10.1007/s00220-018-3144-6.

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30

Avancini, S. S., J. R. Marinelli, D. P. Menezes, M. M. Watanabe de Moraes, and N. Yoshinaga. "Exact Dyson Expansion for a Single J-Shell Within the Quon Algebra." International Journal of Modern Physics E 07, no. 03 (June 1998): 379–87. http://dx.doi.org/10.1142/s0218301398000178.

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The quon algebra, which interpolates between the Bose and Fermi algebras and depends on a free paramenter q, is used to generate a deformed Dyson boson expansion of the quadrupole operator. Then we obtain a quadrupole-quadrupole hamiltonian, for a single j-shell, in terms of this deformed bosonic operator. The hamiltonian is diagonalized and its eigenvalues are compared with the ones obtained from the fermionic quadrupole-quadrupole hamiltonian. The deformation parameter helps in achieving the correct excitation energy levels, what cannot be encountered in practice with the usual non-deformed Dyson expansion.

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31

MARTÍNEZ-MORO, EDGAR. "PROPERTIES OF COMMUTATIVE ASSOCIATION SCHEMES DERIVED BY FGLM TECHNIQUES." International Journal of Algebra and Computation 12, no. 06 (December 2002): 849–65. http://dx.doi.org/10.1142/s021819670200119x.

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Association schemes are combinatorial objects that allow us solve problems in several branches of mathematics. They have been used in the study of permutation groups and graphs and also in the design of experiments, coding theory, partition designs etc. In this paper we show some techniques for computing properties of association schemes. The main framework arises from the fact that we can characterize completely the Bose–Mesner algebra in terms of a zero-dimensional ideal. A Gröbner basis of this ideal can be easily derived without the use of Buchberger algorithm in an efficient way. From this statement, some nice relations arise between the treatment of zero-dimensional ideals by reordering techniques (FGLM techniques) and some properties of the schemes such as P-polynomiality, and minimal generators of the algebra.

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32

Krivsky and Simulik. "Fermi-Bose duality of the Dirac equation and extended real Clifford-Dirac algebra." Condensed Matter Physics 13, no. 4 (2010): 43101. http://dx.doi.org/10.5488/cmp.13.43101.

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33

Buchholz, Detlev. "The Resolvent Algebra of Non-relativistic Bose Fields: Sectors, Morphisms, Fields and Dynamics." Communications in Mathematical Physics 375, no. 2 (January 10, 2020): 1159–99. http://dx.doi.org/10.1007/s00220-019-03629-8.

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34

Matsumoto, Makoto. "A generalization of Jaeger-Nomura's Bose Mesner algebra associated to type II matrices." Annales de l’institut Fourier 49, no. 3 (1999): 1027–35. http://dx.doi.org/10.5802/aif.1704.

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35

DERIGLAZOV, A. A., and A. V. GALAJINSKY. "GEOMETRICAL FORMULATION FOR THE SIEGEL SUPERPARTICLE." Modern Physics Letters A 09, no. 37 (December 7, 1994): 3445–53. http://dx.doi.org/10.1142/s0217732394003270.

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In the superspace zM=(xμ, θR, θL) the global symmetries for d=10 superparticle model with kinetic terms for both Bose and Fermi variables are shown to form a superalgebra, which includes the Poincaré superalgebra as a subalgebra. The subalgebra is realized in the space of variables of the theory by a nonstandard way. The local version of this model with off-shell closed Lagrangian algebra of gauge symmetries and off-shell global supersymmetry are presented. It is shown that the resulting model is dynamically equivalent to the Siegel superparticle.

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Hong-Yi, Fan, and Fan Yue. "New Bose Operator Realization of SU(2) Algebra and Its Application in Optical Propagation." Communications in Theoretical Physics 38, no. 4 (October 15, 2002): 403–6. http://dx.doi.org/10.1088/0253-6102/38/4/403.

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37

Hong-Yi, Fan, and Wang Yong. "Generating Generalized Bessel Equations by Virtue of Bose Operator Algebra and Entangled State Representations." Communications in Theoretical Physics 45, no. 1 (January 2006): 71–74. http://dx.doi.org/10.1088/0253-6102/45/1/013.

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38

Honegger, Reinhard. "Decomposition of Positive Sesquilinear Forms and the Central Decomposition of Gauge-Invariant Quasi-Free States on the Weyl-Algebra." Zeitschrift für Naturforschung A 45, no. 1 (January 1, 1990): 17–28. http://dx.doi.org/10.1515/zna-1990-0105.

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AbstractA decomposition theory for positive sesquilinear forms densely defined in Hilbert spaces is developed. On decomposing such a form into its closable and singular part and using Bochner's theorem it is possible to derive the central decomposition of the associated gauge-invariant quasifree state on the boson C*-Weyl algebra. The appearance of a classical field part of the boson system is studied in detail in the GNS-representation and shown to correspond to the so-called singular subspace of a natural enlargement of the one-boson testfunction space. In the example of Bose-Einstein condensation a non-trivial central decomposition (or equivalently a non-trivial classical field part) is directly related to the occurrence of the condensation phenomenon.

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39

Tungsarote, Rarai. "Some investigations on the Bose–Srivastava algebra related to the multidimensional partially balanced association scheme." Journal of Statistical Planning and Inference 73, no. 1-2 (September 1998): 363–72. http://dx.doi.org/10.1016/s0378-3758(98)00070-6.

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40

FALCO, L. DE, R. MIGNANI, and R. SCIPIONI. "FOCK SPACE FOR GENERALIZED STATISTICS AND BOSON-FERMION SUPERSELECTION RULE." Modern Physics Letters B 10, no. 21 (September 10, 1996): 1035–41. http://dx.doi.org/10.1142/s0217984996001176.

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We introduce a generalized Fock space for a recently proposed operatorial deformation of the Heisenberg-Weyl (HW) algebra, aimed at describing statistics different from the Bose or Fermi ones. The new Fock space is obtained by the tensor product of the usual Fock space and the space spanned by the eigenstates of the deformation operator ĝ. We prove a “statistical Ehrenfest-like theorem”, stating that the expectation values of the ladder operators of the generalized HW algebra — taken in the ĝ-subspace — are creation and annihilation operators defined in the usual Fock space and obeying the ordinary statistics, according to the ĝ-eigenvalues. Moreover, such a “statistics” operator ĝ can be regarded as the generator of a boson-fermion superselection rule. As a consequence, the generalized Fock space decomposes into incoherent sectors, and therefore one gets a density matrix diagonal in the ĝ eigenstates. This leads, under suitable conditions, to the possibility of continuously interpolating between different statistics. In particular, it is necessary to assume a nonstandard Liouville-Von Neumann equation for the density matrix, of the type already considered e.g. in the framework of quantum gravity. It is also preliminarily shown that our formalism leads in a natural way — due to the very properties of the operator ĝ — to a grading of the HW algebra, and therefore to a supersymmetrical scheme.

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41

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

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

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42

MKRTCHYAN, H., and R. MKRTCHYAN. "10D N=1 MASSLESS BPS SUPERMULTIPLETS." Modern Physics Letters A 19, no. 12 (April 20, 2004): 931–44. http://dx.doi.org/10.1142/s0217732304013817.

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We consider d=10, N=1 supersymmetry algebra with maximal number of tensor charges Z and introduce a class of orbits of Z, invariant w.r.t. the T8 subgroup of massless particles' little group T8⋉ SO (8). For that class of orbits we classify all possible orbits and little groups, which appear to be semidirect products T8⋉ SO (k1)×⋯× SO (kn), with k1+⋯+kn=8, where compact factor is embedded into SO (8) by triality map. We define actions of little groups on supercharge Q and construct corresponding supermultiplets. In some particular cases we show the existence of supermultiplets with both Fermi and Bose sectors consisting of the same representations of tensorial Poincaré. In addition, complete classification of supermultiplets (not restricted to T8-invariant orbits) with rank-2 matrix of supersymmetry charges anticommutator, is given.

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DOPLICHER, SERGIO, and GHERARDO PIACITELLI. "ANY COMPACT GROUP IS A GAUGE GROUP." Reviews in Mathematical Physics 14, no. 07n08 (July 2002): 873–85. http://dx.doi.org/10.1142/s0129055x02001430.

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The assignment of the local observables in the vacuum sector, fulfilling the standard axioms of local quantum theory, is known to determine uniquely a compact group G of gauge transformations of the first kind together with a central involutive element k of G, and a complete normal algebra of fields carrying the localizable charges, on which k defines the Bose/Fermi grading. We show here that any such pair {G, k}, where G is compact metrizable, does actually appear. The corresponding model can be chosen to fulfill also the split property. This is not a dynamical phenomenon: a given {G, k} arises as the gauge group of a model where the local algebras of observables are a suitable subnet of local algebras of a possibly infinite product of free field theories.

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44

Jafarizadeh, M. A., R. Sufiani, S. Nami, and M. Golmohammadi. "Bose-Mesner algebra on finite G/H coset graphs and its application on continuous time quantum walks." Quantum Information Processing 11, no. 3 (August 27, 2011): 729–49. http://dx.doi.org/10.1007/s11128-011-0282-6.

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45

Krivsky, I. Yu, T. M. Zajac, and S. Shpyrko. "Extension of the Standard CD Algebra in the Axiomatic Approach for Spinor Field and Fermi–Bose Duality." Advances in Applied Clifford Algebras 27, no. 2 (August 19, 2016): 1431–58. http://dx.doi.org/10.1007/s00006-016-0717-3.

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46

BALACHANDRAN, A. P., G. MANGANO, A. PINZUL, and S. VAIDYA. "SPIN AND STATISTICS ON THE GROENEWOLD–MOYAL PLANE: PAULI-FORBIDDEN LEVELS AND TRANSITIONS." International Journal of Modern Physics A 21, no. 15 (June 20, 2006): 3111–26. http://dx.doi.org/10.1142/s0217751x06031764.

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The Groenewold–Moyal plane is the algebra [Formula: see text] of functions on ℝd+1 with the *-product as the multiplication law, and the commutator [Formula: see text] between the coordinate functions. Chaichian et al.1 and Aschieri et al.2 have proved that the Poincaré group acts as automorphisms on [Formula: see text] if the coproduct is deformed. (See also the prior work of Majid,3 Oeckl4 and Grosse et al.5) In fact, the diffeomorphism group with a deformed coproduct also does so according to the results of Ref. 2. In this paper we show that for this new action, the Bose and Fermi commutation relations are deformed as well. Their potential applications to the quantum Hall effect are pointed out. Very striking consequences of these deformations are the occurrence of Pauli-forbidden energy levels and transitions. Such new effects are discussed in simple cases.

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47

Jafarizadeh, M. A., R. Sufiani, and S. Jafarizadeh. "Recursive calculation of effective resistances in distance-regular networks based on Bose–Mesner algebra and Christoffel–Darboux identity." Journal of Mathematical Physics 50, no. 2 (February 2009): 023302. http://dx.doi.org/10.1063/1.3077145.

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48

LAVAGNO, A., and P. NARAYANA SWAMY. "DEFORMED QUANTUM STATISTICS IN TWO DIMENSIONS." International Journal of Modern Physics B 23, no. 02 (January 20, 2009): 235–50. http://dx.doi.org/10.1142/s0217979209049723.

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It is known from the early work of May in 1964 that ideal Bose gas do not exhibit condensation phenomenon in two dimensions. On the other hand, it is also known that the thermostatistics arising from q-deformed oscillator algebra has no connection with the spatial dimensions of the system. Our recent work concerns the study of important thermodynamic functions such as the entropy, occupation number, internal energy and specific heat in ordinary three spatial dimensions, where we established that such thermostatistics is developed by consistently replacing the ordinary thermodynamic derivatives by the Jackson derivatives. The thermostatistics of q-deformed bosons and fermions in two spatial dimensions is an unresolved question that is the subject of this investigation. We study the principal thermodynamic functions of both bosons and fermions in the two-dimensional q-deformed formalism and we find that, different from the standard case, the specific heat of q-boson and q-fermion ideal gas, at fixed temperature and number of particles, are no longer identical.

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Pavon Torres, Omar, Manuel Davila Davila, and Maximo A. Aguero Granados. "Introduction to the Coherent States Approach for Solving Non-linear Physical Problems." Applied Physics Research 8, no. 1 (January 29, 2016): 106. http://dx.doi.org/10.5539/apr.v8n1p106.

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We summarize some crucial results from mathematical models that help us understand the relevance of gener-alized coherent states (GCS), a fundamental method used for the description of non-linear problems in physics. We mainly concentrate our review in the following models: ferromagnetism, nonlinear Schr¨odinger equation with external potential, nonlinear quantum oscillators, Bose - Einstein condensation (BEC) and the DNA quasi-spin model. Such models and some applications of the wide variety these involve are outlined. As variational trial states, the coherent states (CS) allow the estimation of the ground state energies and properties, yielding results which become exact in a number of nonlinear diﬀerential equations for dynamical variable of each model. Mainly we concentrate our review on two types of coherent states, The ﬁrst one are based on the Heisenberg - Weyl group where it is applied the bosonization eﬀect. The second one is based on the SU(2)/U(1) Lie group. For this case when the Hamiltonian and all physical operators are constructed by the elements of a Lie algebra, the generalized coherent states approach is directly applied without bozonization.

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50

Abdel-Rady, A. S., Samia S. A. Hassan, Abdel-Nasser A. Osman, and Ahmed Salah. "Quantum phase transition and Berry phase of the Dicke model in the presence of the Stark-shift." International Journal of Modern Physics B 31, no. 12 (May 10, 2017): 1750091. http://dx.doi.org/10.1142/s0217979217500916.

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In this paper, we employ the energy surface method to study a system of a two-level atom Bose–Einstein condensate coupled to a high-finesse optical cavity interacting with a single-mode electromagnetic field in the presence of the Stark-shift. The energy surface, the Phase transitions and the Berry phase of the two-level atom in Dicke model are obtained. Employing the Holstein–Primakoff representation of the angular momentum Lie algebra, the coupling line separation of the normal phase and the superradiant phase which occurs in a collection of fluorescent emitters (such as atoms), between a state containing few electromagnetic excitations are studied and a mean field description of the Dicke model is presented. We notice that in the thermodynamic limit, the energy surface takes a simple form for a direct description of the phase transition. Moreover, we show that the Stark-shift parameters and the atom–atom interactions can strongly affect the phase transition point. The results in the absence of the Stark-shift agree precisely with those obtained by Li, Liu and Zhou, who studied the same model using a different method.

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