ON THE NONCOMMUTATIVE GEOMETRY IN QUANTUM MECHANICS

被引：14

作者：

Haouam, Ilyas ^{[1
]}

机构：

[1] Univ Freres Mentouri, Lab Phys Math & Phys Subatom LPMPS, Constantine, Algeria

来源：

JOURNAL OF PHYSICAL STUDIES | 2020年 / 24卷 / 02期

关键词：

noncommutative geometry; noncommutative quantum mechanics; Weyl quantization; Moyal-Weyl product; Bopp-shift transformation; Seiberg-Witten maps; Weyl-Wigner maps; uncertainty relations; SPACE-TIME; PHASE; FIELD; MODEL;

D O I：

10.30970/jps.24.2002

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we presented and reviewed a formalism that plays a central role in most of the investigations concerning noncommutative geometry. We presented existing methods that successfully allow us to utilize and apply the noncommutativity of phase-space in both quantum mechanics and quantum field theory. In particular, we briefly explained the Weyl quantization, the Moyal-Weyl product, the Bopp-shift transformations, and the Seiberg-Witten maps.

引用

页数：15

共 38 条

[1] Arivoli S., 2016, INT J MOSQ RES, V3, P18
[2] M theory as a matrix model: A conjecture
Banks, T
Fischler, W
Shenker, SH
Susskind, L
[J]. PHYSICAL REVIEW D, 1997, 55 (08): : 5112 - 5128
[3] Berry phase in the gravitational quantum well and the Seiberg-Witten map
Bastos, C.
Bertolami, O.
[J]. PHYSICS LETTERS A, 2008, 372 (34) : 5556 - 5559
[4] Noncommutative gravitational quantum well -: art. no. 025010
Bertolami, O
Rosa, JG
de Aragao, CML
Castorina, P
Zappalà, D
[J]. PHYSICAL REVIEW D, 2005, 72 (02): : 1 - 9
[5] The standard model on non-commutative space-time
Calmet, X
Jurco, B
Schupp, P
Wess, J
Wohlgenannt, M
[J]. EUROPEAN PHYSICAL JOURNAL C, 2002, 23 (02): : 363 - 376
[6] Noncommutative field theory and Lorentz violation
Carroll, SM
Harvey, JA
Kostelecky, VA
Lane, CD
Okamoto, T
[J]. PHYSICAL REVIEW LETTERS, 2001, 87 (14) : 141601/1 - 141601/4
[7] Connes A., 1985, Inst. Hautes Etudes Sci. Publ. Math., V62, P41
[8] Magnetic fields in noncommutative quantum mechanics
Delduc, F.
Duret, Q.
Gieres, F.
Lefrancois, M.
[J]. INTERNATIONAL CONFERENCE ON NONCOMMUTATIVE GEOMETRY AND PHYSICS, 2008, 103
[9] Noncommutative quantum mechanics in a time-dependent background
Dey, Sanjib
Fring, Andreas
[J]. PHYSICAL REVIEW D, 2014, 90 (08):
[10] Fidanza S., 2003, THESIS ECOLE POLYTEC

← 1 2 3 4 →