The generalized Heisenberg group arising from Weyl relations

被引：0
|
作者：
Rebei H. [1 ]
机构：
[1] Department of Mathematics, College of Science, Qassim University, P.O.Box 5155, Buraidah
来源：
Quantum Studies: Mathematics and Foundations | 2015年 / 2卷 / 4期
关键词：
Generalized Heisenberg group; Generalized Weyl operator; Oscillator algebra;
D O I：
10.1007/s40509-015-0054-6
中图分类号：
学科分类号：
摘要：
In this paper, we introduce the generalized Weyl operators canonically associated with the one-mode oscillator Lie algebra as unitary operators acting on the bosonic Fock space Γ (C). Next, we establish the generalized Weyl relations and deduce a group structure on the manifold R2× [- π, π[× R generalizing the well-known Heisenberg one in a natural way. © 2015, Chapman University.
引用
收藏
页码：449 / 466
页数：17
相关论文
共 50 条
  • [21] An affine Weyl group characterization of polynomial Heisenberg algebras
    Morales-Salgado, Vicente Said
    ANNALS OF PHYSICS, 2022, 444
  • [22] REFLECTION GROUP RELATIONS ARISING FROM CLUSTER ALGEBRAS
    Seven, Ahmet I.
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (11) : 4641 - 4650
  • [23] TOPOLOGY OF COUNTABLE SUBGROUPS OF THE HEISENBERG-WEYL GROUP
    BOON, MH
    MCCARTHY, PJ
    PHYSICA A, 1982, 114 (1-3): : 424 - 427
  • [24] ON THE REPRESENTATIONS OF GLQ(N) USING THE HEISENBERG-WEYL RELATIONS
    CHAKRABARTI, R
    JAGANNATHAN, R
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1991, 24 (08): : 1709 - 1720
  • [25] Generalized Coherent States for Polynomial Weyl-Heisenberg Algebras
    Kibler, Maurice R.
    Daoud, Mohammed
    PROCEEDINGS OF THE PHYSICS CONFERENCE TIM - 11, 2012, 1472 : 60 - 69
  • [26] On Proximal Relations in Transformation Semigroups Arising from Generalized Shifts
    Zadeh Shirazi, Fatemah Ayatollah
    Fallahpour, Amir
    Mardanbeigi, Mohammad Reza
    Ahmadabadi, Zahra Nili
    ANALYSIS IN THEORY AND APPLICATIONS, 2022, 38 (01): : 110 - 120
  • [27] Magnetic curves in the generalized Heisenberg group
    Munteanu, Marian Ioan
    Nistor, Ana Irina
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2022, 214
  • [28] ANALYSIS ON A GENERALIZED HEISENBERG-GROUP
    BARKER, SR
    SALAMON, SM
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1983, 28 (AUG): : 184 - 192
  • [29] Local solvability of Laplacian difference operators arising from the discrete Heisenberg group
    Kornelson, KA
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2005, 57 (03): : 598 - 615
  • [30] THE HEISENBERG-WEYL GROUP ON THE ZNXZN DISCRETIZED TORUS MEMBRANE
    FLORATOS, EG
    PHYSICS LETTERS B, 1989, 228 (03) : 335 - 340
12345