Deformation quantization with minimal length

2017/06/03 by Ziemowit Domański, Maciej Błaszak, Domański, Ziemowit +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1706.00980

27 pages, 3 figures

arxiv created 2018/07/30 · arxiv updated 2018/07/31

Abstract

We develop a complete theory of non-formal deformation quantization exhibiting a nonzero minimal uncertainty in position. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on which the star-product is well defined. Basic properties of the star-product are proved and the extension of the star-product to a certain Hilbert space and an algebra of distributions is given. A C*-algebra of observables and a space of states are constructed. Moreover, an operator representation in momentum space is presented. Finally, examples of position eigenvectors and states of maximal localization are given.

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