Remarks on the formulation of quantum mechanics on noncommutative phase spaces

被引:7
作者
Muthukumar, Balasundaram [1 ]
机构
[1] Saha Inst Nucl Phys, 1 AF, Kolkata 700064, W Bengal, India
来源
JOURNAL OF HIGH ENERGY PHYSICS | 2007年 / 01期
关键词
statistical methods; non-commutative geometry;
D O I
10.1088/1126-6708/2007/01/073
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and also with canonically conjugate momenta. With a postulated normalized distribution function in the quantum domain, the square of the Dirac delta density distribution in the classical case is properly realised in noncommutative phase space and it serves as the quantum condition. With only these inputs, we pull out the entire formalisms of noncommutative quantum mechanics in phase space and in Hilbert space, and elegantly establish the link between classical and quantum formalisms and between Hilbert space and phase space formalisms of noncommutative quantum mechanics. Also, we show that the distribution function in this case possesses 'twisted' Galilean symmetry.
引用
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页数:25
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共 38 条
[1]   Noncommutative field theory: Nonrelativistic fermionic field coupled to the Chern-Simons field in 2+1 dimensions [J].
Anacleto, MA ;
Gomes, M ;
da Silva, AJ ;
Spehler, D .
PHYSICAL REVIEW D, 2005, 71 (10)
[2]  
Awata H, 2001, J HIGH ENERGY PHYS
[3]   FORMULATION OF QUANTUM MECHANICS BASED ON THE QUASI-PROBABILITY DISTRIBUTION INDUCED ON PHASE SPACE [J].
BAKER, GA .
PHYSICAL REVIEW, 1958, 109 (06) :2198-2206
[4]  
Barbosa GD, 2003, J HIGH ENERGY PHYS
[5]   DEFORMATION THEORY AND QUANTIZATION .1. DEFORMATIONS OF SYMPLECTIC STRUCTURES [J].
BAYEN, F ;
FLATO, M ;
FRONSDAL, C ;
LICHNEROWICZ, A ;
STERNHEIMER, D .
ANNALS OF PHYSICS, 1978, 111 (01) :61-110
[6]   Hydrogen atom spectrum and the Lamb shift in noncommutative QED [J].
Chaichian, M ;
Sheikh-Jabbari, MM ;
Tureanu, A .
PHYSICAL REVIEW LETTERS, 2001, 86 (13) :2716-2719
[7]   Twisted Galilean symmetry and the Pauli principle at low energies [J].
Chakraborty, Biswajit ;
Gangopadhyay, Sunandan ;
Hazra, Arindam Ghosh ;
Scholtz, Frederik G. .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (30) :9557-9572
[8]  
COURANT R, 1953, METHODS MATH PHYS, P130
[9]   Features of time-independent Wigner functions [J].
Curtright, T ;
Fairlie, D ;
Zachos, C .
PHYSICAL REVIEW D, 1998, 58 (02)
[10]   Classical and quantum Nambu mechanics [J].
Curtright, T ;
Zachos, C .
PHYSICAL REVIEW D, 2003, 68 (08)