The Noncommutative Harmonic Oscillator Based on Symplectic Representation of Galilei Group

被引：10
作者：
Amorim, R. G. G. [1 ,2 ]
Ulhoa, S. C. [2 ]
Santana, A. E. [3 ]
机构：
[1] Inst Fed Educ Ciencia & Tecnol Goias, BR-72811580 Luziania, Goias, Brazil
[2] Univ Brasilia, Fac Gama, BR-72444240 Brasilia, DF, Brazil
[3] Univ Brasilia, Inst Fis, BR-70910900 Brasilia, DF, Brazil
来源：
BRAZILIAN JOURNAL OF PHYSICS | 2013年 / 43卷 / 1-2期
关键词：
Moyal product; Phase space; Quantum fields; QUANTUM-MECHANICS; PHOTON DISTRIBUTION; WIGNER FUNCTIONS; PHASE-SPACE; FIELD; QUANTIZATION; GEOMETRY; ALGEBRA; MODEL;
D O I：
10.1007/s13538-013-0119-0
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We study symplectic unitary representations for the Galilei group and derive the Schrodinger equation in phase space. Our formalism is based on the noncommutative structure of the star product. Guided by group theoretical concepts, we construct a physically consistent phase-space theory in which each state is described by a quasi-probability amplitude associated with the Wigner function. As applications, we derive the Wigner functions for the 3D harmonic oscillator and the noncommutative oscillator in phase space.
引用
收藏
页码：78 / 85
页数：8
相关论文
共 46 条
  • [1] Wigner functions for curved spaces. I. On hyperboloids
    Alonso, MA
    Pogosyan, GS
    Wolf, KB
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2002, 43 (12) : 5857 - 5871
  • [2] Non-commutative geometry and symplectic field theory
    Amorim, R. G. G.
    Fernandes, M. C. B.
    Khanna, F. C.
    Santana, A. E.
    Vianna, J. D. M.
    [J]. PHYSICS LETTERS A, 2007, 361 (06) : 464 - 471
  • [3] Perturbative symplectic field theory and Wigner function
    Amorim, Ronni G. G.
    Khanna, Faqir C.
    Santana, Ademir E.
    Vianna, Jose David M.
    [J]. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2009, 388 (18) : 3771 - 3778
  • [4] Poincare-Lie algebra and relativistic phase space
    Andrade, MCB
    Santana, AE
    Vianna, JDM
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2000, 33 (22): : 4015 - 4024
  • [5] THE NONCOMMUTATIVE GEOMETRY OF THE QUANTUM HALL-EFFECT
    BELLISSARD, J
    VANELST, A
    SCHULZBALDES, H
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 1994, 35 (10) : 5373 - 5451
  • [6] ON A QUANTUM ALGEBRAIC APPROACH TO A GENERALIZED PHASE-SPACE
    BOHM, D
    HILEY, BJ
    [J]. FOUNDATIONS OF PHYSICS, 1981, 11 (3-4) : 179 - 203
  • [7] What are the bounds on space-time non-commutativity?
    Calmet, X
    [J]. EUROPEAN PHYSICAL JOURNAL C, 2005, 41 (02): : 269 - 272
  • [8] The spectral action principle
    Chamseddine, AH
    Connes, A
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 186 (03) : 731 - 750
  • [9] GRAVITY IN NONCOMMUTATIVE GEOMETRY
    CHAMSEDDINE, AH
    FELDER, G
    FROHLICH, J
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1993, 155 (01) : 205 - 217
  • [10] Connes A., 1991, Nuclear Physics B, Proceedings Supplements, V18B, P29, DOI 10.1016/0920-5632(91)90120-4
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