An exact representation isotropic and anisotropic noncommutative phase spaces, and their relations

2014/03/10 by Hiroshi Kakuhata, H. Kakuhata, M. Nakamura +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Advanced Operator Algebra Research #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.1403.2171

12 pages, added references for section 1

arxiv created 2014/03/19 · arxiv updated 2014/03/20

Abstract

Noncommutative phase space of an arbitrary dimension is considered. The both of operators coordinates and momenta in noncommutative phase space may be noncommutative. In this paper, we introduce momentum-momentum noncommutativity in addition to coordinate-coordinate noncommutativity. We find an exact form for the linear coordinate transformation which relates a noncommutative phase space to the corresponding ordinary one. As an example, the Hamiltonian of a three-dimensional harmonic oscillator is examined.

Related

• Representation of noncommutative phase space
• Harmonic oscillator on noncommutative spaces
• Non-Hermitian two-dimensional harmonic oscillator in noncommutative phase-space
• Non-commutative phase space and its space-time symmetry
• Spectrum of the harmonic oscillator in a general noncommutative phase space