A comparative review of four formulations of noncommutative quantum mechanics

被引：80
作者：
Gouba, Laure [1 ]
机构：
[1] Abdus Salam Int Ctr Theoret Phys ICTP, Str Costiera 11, I-34151 Trieste, Italy
来源：
INTERNATIONAL JOURNAL OF MODERN PHYSICS A | 2016年 / 31卷 / 19期
关键词：
Noncommutative geometry; noncommutative quantum mechanics; formalism; star product; Bopp's shift; Seiberg-Witten map; path-integral; Weyl-Wigner transform; FIELD-THEORY; LANDAU PROBLEM; REPRESENTATIONS; PLANE; PHASE; SCATTERING; SPECTRUM;
D O I：
10.1142/S0217751X16300258
中图分类号：
O57 [原子核物理学、高能物理学];
学科分类号：
070202 ;
摘要：
Four formulations of quantum mechanics on noncommutative Moyal phase spaces are reviewed. These are the canonical, path-integral, Weyl-Wigner and systematic formulations. Although all these formulations represent quantum mechanics on a phase space with the same deformed Heisenberg algebra, there are mathematical and conceptual differences which we discuss.
引用
收藏
页数：15
相关论文
共 92 条
[21]   Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space [J].
Benatti, Fabio ;
Gouba, Laure .
OPEN SYSTEMS & INFORMATION DYNAMICS, 2015, 22 (04)
[22]   Classical limits of quantum mechanics on a non-commutative configuration space [J].
Benatti, Fabio ;
Gouba, Laure .
JOURNAL OF MATHEMATICAL PHYSICS, 2013, 54 (06)
[23]   Scaling of variables and the relation between noncommutative parameters in noncommutative quantum mechanics [J].
Bertolami, O ;
Rosa, JG ;
de Aragao, CML ;
Castorina, P ;
Zappalà, D .
MODERN PHYSICS LETTERS A, 2006, 21 (10) :795-802
[24]   Aspects of phase-space noncommutative quantum mechanics [J].
Bertolami, O. ;
Leal, P. .
PHYSICS LETTERS B, 2015, 750 :6-11
[25]   Perturbative analysis of the Seiberg-Witten map [J].
Bichl, AA ;
Grimstrup, JM ;
Popp, L ;
Schweda, M ;
Wulienhaar, R .
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 2002, 17 (16) :2219-2231
[26]  
Bopp F., 1956, Ann. l'inst. Henri Poincare, V15, P81
[27]   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
[28]   Quantum field theory on non-commutative space-times and the persistence of ultraviolet divergences [J].
Chaichian, M ;
Demichev, A ;
Presnajder, P .
NUCLEAR PHYSICS B, 2000, 567 (1-2) :360-390
[29]   Aharonov-Bohm effect in noncommutative spaces [J].
Chaichian, M ;
Presnajder, P ;
Sheikh-Jabbari, MM ;
Tureanu, A .
PHYSICS LETTERS B, 2002, 527 (1-2) :149-154
[30]   Gauge covariance of the Aharonov-Bohm phase in noncommutative quantum mechanics [J].
Chaichian, Masud ;
Langvik, Miklos ;
Sasaki, Shin ;
Tureanu, Anca .
PHYSICS LETTERS B, 2008, 666 (02) :199-204
12345678910