Sicong Jing et al JHEP10(2004)049 doi:10.1088/1126-6708/2004/10/049
Deformation quantization of noncommutative quantum mechanics
Sicong Jing1, Fen Zuo1 and Taihua Heng1
Show affiliationsThe Wigner phase-space distribution function provides the basis for Moyal's deformation quantization alternative to the more conventional Hilbert space and path integral quantization. In this paper, we investigate the basic aspects of deformation quantization for noncommutative quantum mechanics (NCQM). We first prove some general relations of the Weyl correspondence in non-commuting phase-space. Then we derive explicit form of the Wigner Function (WF) for NCQM starting from fundamental principle of the Weyl correspondence, and show that it satisfies a generalized 
-genvalue equation. We also demonstrate that the new WFs possess orthonormality and completeness, so they can be used as a basis to expand all phase-space functions. Some example is discussed to support our results.
- Keywords
- PACS
- Subjects
- Dates
-
Issue 10 (October 2004)
Received 7 July 2004, accepted for publication 21 October 2004
Published 9 November 2004
-
Deformation quantization of noncommutative quantum mechanics
Sicong Jing et al JHEP10(2004)049
-
Probing supernova shock waves and neutrino flavour transitions in next-generation water Cherenkov detectors
G L Fogli et al JCAP04(2005)002
-
Results of the regional key comparison EUROMET.M.P-K1.a in the pressure range from 0.1 Pa to 1000 Pa
Anita Calcatelli et al 2005 Metrologia 42 07004
-
Combined constraints on Cardassian models from supernovae, cosmic microwave background and large scale structure observations
M Amarzguioui et al JCAP01(2005)008
-
Self-patterned aluminium interconnects and ring electrodes for arrays of microcavity plasma devices encapsulated in Al2O3
K S Kim et al 2008 J. Phys. D: Appl. Phys. 41 012004
-
Ultra-high vacuum scanning tunnelling microscopy investigation of free radical adsorption to the Si(111)-7 × 7 surface
Nathan P Guisinger et al 2007 Nanotechnology 18 044011
-
Measurement of the lattice parameter of a silicon crystal
E Massa et al 2009 New J. Phys. 11 053013
-
Hydrophobic coating of microfluidic chips structured by SU-8 polymer for segmented flow operation
J T Schumacher et al 2008 J. Micromech. Microeng. 18 055019
-
Condensation of isolated semi-flexible filaments driven by depletion interactions
A. W. C. Lau et al 2009 EPL 87 48006
-
Records in a changing world
Joachim Krug J. Stat. Mech. (2007) P07001
Related review articles
What's this?- Experimental quantum simulations of many-body physics with trapped ions
- Quasi-probability representations of quantum theory with applications to quantum information science
- Essential entanglement for atomic and molecular physics