Deformation quantization with minimal length
Mathematical Physics
2018-07-31 v2 math.MP
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.
Cite
@article{arxiv.1706.00980,
title = {Deformation quantization with minimal length},
author = {Ziemowit Domański and Maciej Błaszak},
journal= {arXiv preprint arXiv:1706.00980},
year = {2018}
}
Comments
27 pages, 3 figures