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Journal articles on the topic 'Bose algebras'

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Published: 4 June 2021
Last updated: 26 January 2023

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1

Słowikowski, W. "Ultracoherence in Bose algebras." Advances in Applied Mathematics 9, no. 4 (December 1988): 377–427. http://dx.doi.org/10.1016/0196-8858(88)90020-6.

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2

BANG, HA HUY. "GENERALIZED DEFORMED PARA-BOSE OSCILLATOR AND NONLINEAR ALGEBRAS." Modern Physics Letters A 10, no. 36 (November 30, 1995): 2739–48. http://dx.doi.org/10.1142/s0217732395002878.

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Generalized deformed commutation relations for a single mode para-Bose oscillator and for a system of two para-Bose oscillators are constructed. It turns out that generalized deformed para-Bose oscillators are not, in general, exactly independent. Furthermore, we also discuss about the Fock space corresponding to generalized deformed para-Bose oscillators. Finally, we show how SU(2) and SU(1, 1) generators can be constructed in terms of generalized deformed para-Bose creation and annihilation operators. The algebras SU(2) and SU(1, 1) of generalized deformed oscillators14,18 are the special cases of generalized deformed para-Bose oscillators algebras but, interestingly, they have the same form.
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3

Koppinen, M. "On Algebras with Two Multiplications, Including Hopf Algebras and Bose–Mesner Algebras." Journal of Algebra 182, no. 1 (May 1996): 256–73. http://dx.doi.org/10.1006/jabr.1996.0170.

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4

Nomura, Kazumasa. "Spin Models and Bose–Mesner Algebras." European Journal of Combinatorics 20, no. 7 (October 1999): 691–700. http://dx.doi.org/10.1006/eujc.1999.0315.

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5

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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6

Chan, Ada, and Chris Godsil. "Bose–Mesner algebras attached to invertible Jones pairs." Journal of Combinatorial Theory, Series A 106, no. 2 (May 2004): 165–91. http://dx.doi.org/10.1016/j.jcta.2004.01.007.

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7

HALPERN, M. B., and C. SCHWARTZ. "THE ALGEBRAS OF LARGE N MATRIX MECHANICS." International Journal of Modern Physics A 14, no. 19 (July 30, 1999): 3059–119. http://dx.doi.org/10.1142/s0217751x99001482.

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Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: the Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.
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8

MELJANAC, STJEPAN, and ANTE PERICA. "GENERALIZED QUON STATISTICS." Modern Physics Letters A 09, no. 35 (November 20, 1994): 3293–99. http://dx.doi.org/10.1142/s0217732394003117.

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Generalized quons interpolating between Bose, Fermi, para-Bose, para-Fermi and anyonic statistics are proposed. They follow from the R-matrix approach to deformed associative algebras. It is proved that generalized quons have the same main properties as quons. A new result for the number operator is presented and some physical features of generalized quons are discussed in the limit [Formula: see text].
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9

Bannai, Etsuko. "Bose-Mesner Algebras Associated with Four-Weight Spin Models." Graphs and Combinatorics 17, no. 4 (December 2001): 589–98. http://dx.doi.org/10.1007/pl00007251.

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10

Curtin, Brian. "Inheritance of hyper-duality in imprimitive Bose–Mesner algebras." Discrete Mathematics 308, no. 14 (July 2008): 3003–17. http://dx.doi.org/10.1016/j.disc.2007.08.025.

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11

Schmitt, H. A., P. Halse, B. R. Barrett, and A. B. Balantekin. "Orthosymplectic supersymmetry complementary to combined Bose-Fermi seniority algebras." Physics Letters B 210, no. 1-2 (August 1988): 1–4. http://dx.doi.org/10.1016/0370-2693(88)90336-x.

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12

Blau, Harvey I. "Integral Table Algebras and Bose–Mesner Algebras with a Faithful Nonreal Element of Degree Three." Journal of Algebra 231, no. 2 (September 2000): 484–545. http://dx.doi.org/10.1006/jabr.1999.8188.

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13

Mickelsson, Jouko. "Bose-Fermi correspondence and Kac-Moody algebras in four dimensions." Physical Review D 32, no. 2 (July 15, 1985): 436–39. http://dx.doi.org/10.1103/physrevd.32.436.

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14

Steeb, W. H., and N. Euler. "Nonlinear dynamical systems, first integrals, Bose operators, and Lie algebras." Foundations of Physics Letters 3, no. 4 (August 1990): 367–74. http://dx.doi.org/10.1007/bf00769708.

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15

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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16

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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17

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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18

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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19

Martin, William J. "Scaffolds: A graph-theoretic tool for tensor computations related to Bose-Mesner algebras." Linear Algebra and its Applications 619 (June 2021): 50–106. http://dx.doi.org/10.1016/j.laa.2021.02.009.

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20

Sankey, A. D. "Type-II matrices in weighted Bose–Mesner algebras of ranks 2 and 3." Journal of Algebraic Combinatorics 32, no. 1 (December 4, 2009): 133–53. http://dx.doi.org/10.1007/s10801-009-0209-9.

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21

ISAAC, P. S., W. P. JOYCE, and J. LINKS. "AN ALGEBRAIC APPROACH TO SYMMETRIC PRE-MONOIDAL STATISTICS." Journal of Algebra and Its Applications 06, no. 01 (February 2007): 49–69. http://dx.doi.org/10.1142/s0219498807002065.

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Recently, generalized Bose–Fermi statistics was studied in a category theoretic framework and to accommodate this endeavor the notion of a pre-monoidal category was developed. Here we describe an algebraic approach for the construction of such categories. We introduce a procedure called twining which breaks the quasi-bialgebra structure of the universal enveloping algebras of semi-simple Lie algebras and renders the category of finite-dimensional modules pre-monoidal. The category is also symmetric, meaning that each object of the category provides representations of the symmetric groups, which allows for a generalized boson-fermion statistic to be defined. Exclusion and confinement principles for systems of indistinguishable particles are formulated as an invariance with respect to the actions of the symmetric group. We apply the procedure to suggest that the symmetries which can be associated to color, spin and flavor degrees of freedom lead to confinement of states.
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22

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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23

Jafarizadeh, M. A., and S. Salimi. "Investigation of continuous-time quantum walk via modules of Bose–Mesner and Terwilliger algebras." Journal of Physics A: Mathematical and General 39, no. 42 (October 4, 2006): 13295–323. http://dx.doi.org/10.1088/0305-4470/39/42/007.

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24

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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25

Green, HS. "Statistical Symmetries in Physics." Australian Journal of Physics 47, no. 2 (1994): 109. http://dx.doi.org/10.1071/ph940109.

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Every law of physics is invariant under some group of transformations and is therefore the expression of some type of symmetry. Symmetries are classified as geometrical, dynamical or statistical. At the most fundamental level, statistical symmetries are expressed in the field theories of the elementary particles. This paper traces some of the developments from the discovery of Bose statistics, one of the two fundamental symmetries of physics. A series of generalizations of Bose statistics is described. A supersymmetric generalization accommodates fermions as well as bosons, and further generalizations, including parastatistics, modular statistics and graded statistics, accommodate particles with properties such as 'colour'. A factorization of elements of ggl (nb' n f) can be used to define truncated boson operators. A general construction is given for q-deformed boson operators, and explicit constructions of the same type are given for various 'deformed' algebras; these include a rather simple Q-deformed variety as well as the well known q-deformed variety. A summary is given of some of the applications and potential applications.
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26

Accardi, Luigi, and Carlo Pandiscia. "Mathematical aspects of Bose–Einstein condensation in equilibrium and local equilibrium conditions." Infinite Dimensional Analysis, Quantum Probability and Related Topics 20, no. 04 (December 2017): 1750024. http://dx.doi.org/10.1142/s0219025717500242.

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In the paper4 the notion of local KMS condition, introduced in Ref. 3 and extended in Ref. 2, was shown to open new possibilities in the study of the problem of Bose–Einstein Condensation (BEC). In this paper we analyze the general structure of states on the CCR algebra over a pre-Hilbert space that satisfies the local KMS condition with respect to a free Hamiltonian [Formula: see text] and to a given inverse temperature function [Formula: see text]. The replacement of Hilbert space by a pre-Hilbert space allows one to deal with test functions more singular than those usually considered in the theory of distributions (thus allowing e.g., fractal critical surfaces) and is equivalent (in the language of Weyl algebras) to consider a degenerate symplectic form. It is precisely this degeneracy that allows one to introduce in an intrinsic way the notions of [Formula: see text]-critical subspace (resp. [Formula: see text]-critical surface) and of states exhibiting BEC, independently of infinite volume limits and of boundary conditions. We prove that the covariance of any local KMS state is uniquely determined by the pair [Formula: see text], through a nonlinear extension of the Planck factor. For a large class of such states (including all known examples) the covariance splits into a sum of two mutually singular terms: one corresponding to a regular state, the other one with support on a critical surface (or more generally a critical subspace) uniquely determined by [Formula: see text] and [Formula: see text]. In particular we prove that, if such a state is gauge invariant Gaussian (quasi-free), then the [Formula: see text]-equilibrium condition uniquely determines the regular part of the state, while the singular part is arbitrary.
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27

TZE, CHIA-HSIUNG. "MANIFOLD-SPLITTING REGULARIZATION, SELF-LINKING, TWISTING, WRITHING NUMBERS OF SPACE-TIME RIBBONS and POLYAKOV’S PROOF OF FERMI-BOSE TRANSMUTATIONS." International Journal of Modern Physics A 03, no. 08 (August 1988): 1959–79. http://dx.doi.org/10.1142/s0217751x88000825.

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We present an alternative formulation of Polyakov’s regularization of Gauss’ integral formula for a single closed Feynman path. A key element in his proof of the D=3 fermi-bose transmutations induced by topological gauge fields, this regularization is linked here with the existence and properties of a nontrivial topological invariant for a closed space ribbon. This self-linking coefficient, an integer, is the sum of two differential characteristics of the ribbon, its twisting and writhing numbers. These invariants form the basis for a physical interpretation of our regularization. Their connection to Polyakov’s spinorization is discussed. We further generalize our construction to the self-linking, twisting and writhing of higher dimensional d=n (odd) submanifolds in D=(2n+1) space-time. Our comprehensive analysis intends to supplement Polyakov’s work as it identifies a natural path to its higher dimensional mathematical and physical generalizations. Combining the theorems of White on self-linking of manifolds and of Adams on nontrivial Hopf fibre bundles and the four composition-division algebras, we argue that besides Polyakov’s case where (d, D)=(1, 3) tied to complex numbers, the potentially interesting extensions are two chiral models with (d, D)=(3, 7) and (7, 15) uniquely linked to quaternions and octonions. In Memoriam Richard P. Feynman
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28

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

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We show that the Yang-Baxter equations for two-dimensional models admit as a group of symmetry the infinite discrete group [Formula: see text]. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. We show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. We indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiate the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non-trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. We mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. Our results also yield the generalization of the condition qn=1 so often mentioned in the theory of quantum groups, when no q parameter is available.
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29

Praeger, Cheryl, and Prabir Bhattacharya. "Circulant association schemes on triples." New Zealand Journal of Mathematics 52 (September 19, 2021): 153–65. http://dx.doi.org/10.53733/106.

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Association Schemes and coherent configurations (and the related Bose-Mesner algebra and coherent algebras) are well known in combinatorics with many applications. In the 1990s, Mesner and Bhattacharya introduced a three-dimensional generalisation of association schemes which they called an {\em association scheme on triples} (AST) and constructed examples of several families of ASTs. Many of their examples used 2-transitive permutation groups: the non-trivial ternary relations of the ASTs were sets of ordered triples of pairwise distinct points of the underlying set left invariant by the group; and the given permutation group was a subgroup of automorphisms of the AST. In this paper, we consider ASTs that do not necessarily admit 2-transitive groups as automorphism groups but instead a transitive cyclic subgroup of the symmetric group acts as automorphisms. Such ASTs are called {\em circulant} ASTs and the corresponding ternary relations are called {\em circulant relations}. We give a complete characterisation of circulant ASTs in terms of AST-regular partitions of the underlying set. We also show that a special type of circulant, that we call a {\em thin circulant}, plays a key role in describing the structure of circulant ASTs. We outline several open questions.
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30

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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31

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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32

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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33

Christensen, Martin S. "Regularity of Villadsen algebras and characters on their central sequence algebras." MATHEMATICA SCANDINAVICA 123, no. 1 (August 1, 2018): 121–41. http://dx.doi.org/10.7146/math.scand.a-104840.

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We show that if $A$ is a simple Villadsen algebra of either the first type with seed space a finite dimensional CW complex, or of the second type, then $A$ absorbs the Jiang-Su algebra tensorially if and only if the central sequence algebra of $A$ does not admit characters.Additionally, in a joint appendix with Joan Bosa (see the following paper), we show that the Villadsen algebra of the second type with infinite stable rank fails the Corona Factorization Property, thus providing the first example of a unital, simple, separable and nuclear $C^\ast $-algebra with a unique tracial state which fails to have this property.
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34

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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35

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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36

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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37

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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38

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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39

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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40

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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41

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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42

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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43

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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44

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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45

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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46

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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47

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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48

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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49

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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50

Wang, Mingsheng, and Dengguo Feng. "On Lin–Bose problem." Linear Algebra and its Applications 390 (October 2004): 279–85. http://dx.doi.org/10.1016/j.laa.2004.04.020.

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