A unifying perspective on the Moyal and Voros products and their physical meanings
Abstract
The Moyal and Voros formulations of non-commutative quantum field theory have been a point of controversy in the recent past. Here we address this issue in the context of non-commutative non-relativistic quantum mechanics. In particular, we show that the two formulations simply correspond to two different representations associated with two different choices of basis on the quantum Hilbert space. From a mathematical perspective, the two formulations are therefore completely equivalent, but we also argue that only the Voros formulation admits a consistent physical interpretation. These considerations are elucidated by considering the free-particle transition amplitude in the two representations.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- July 2011
- DOI:
- 10.1088/1751-8113/44/28/285204
- arXiv:
- arXiv:1101.2495
- Bibcode:
- 2011JPhA...44B5204B
- Keywords:
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- High Energy Physics - Theory;
- Quantum Physics
- E-Print:
- 10 pages