A unifying perspective on the Moyal and Voros products and their physical meanings
Date
2011
Authors
Basu P.
Chakraborty B.
Scholtz F.G.
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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. © 2011 IOP Publishing Ltd.
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Journal of Physics A: Mathematical and Theoretical
44
28
http://www.scopus.com/inward/record.url?eid=2-s2.0-79960040183&partnerID=40&md5=2e12dde3d7e31f6e586f894975c6390c
44
28
http://www.scopus.com/inward/record.url?eid=2-s2.0-79960040183&partnerID=40&md5=2e12dde3d7e31f6e586f894975c6390c