A Deformation Quantization Theory for Non-Commutative Quantum Mechanics

Details A Deformation Quantization Theory for Non-Commutative Quantum Mechanics A Deformation Quantization Theory for Non-Commutative Quantum Mechanics

2009-11-06

arxiv.org/abs/0911.1209v1

J.Math.Phys.51:072101,2010

Physics

Mathematical Physics

Submitted for publication

Scientific paper

10.1063/1.3436581

We show that the deformation quantization of non-commutative quantum
mechanics previously considered by Dias and Prata can be expressed as a Weyl
calculus on a double phase space. We study the properties of the star-product
thus defined, and prove a spectral theorem for the star-genvalue equation using
an extension of the methods recently initiated by de Gosson and Luef.

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