On second quantization on noncommutative spaces with twisted symmetries
Abstract
By application of the general twist-induced star-deformation procedure we translate second quantization of a system of bosons/fermions on a symmetric spacetime in a non-commutative language. The procedure deforms in a coordinated way the spacetime algebra and its symmetries, the wave-mechanical description of a system of n bosons/fermions, the algebra of creation and annihilation operators and also the commutation relations of the latter with functions of spacetime; our key requirement is the mode-decomposition independence of the quantum field. In a conservative view, the use of noncommutative coordinates can be seen just as a way to better express non-local interactions of a special kind. In a non-conservative one, we obtain a covariant framework for QFT on the corresponding noncommutative spacetime consistent with quantum mechanical axioms and Bose-Fermi statistics. One distinguishing feature is that the field commutation relations remain of the type "field (anti)commutator=a distribution". We illustrate the results by choosing as examples interacting non-relativistic and free relativistic QFT on Moyal space(time)s.
Cite
@article{arxiv.0811.0773,
title = {On second quantization on noncommutative spaces with twisted symmetries},
author = {Gaetano Fiore},
journal= {arXiv preprint arXiv:0811.0773},
year = {2020}
}
Comments
Latex file, 45 pages. I have corrected a small typo present in 3 points of the previous version and in the version published also in JPA (which had occurred via late careless serial replacements, with no consequences on the results of the calculations): $\beta^*=\beta^{-1}$ has been corrected into $\beta^*=S(\beta^{-1})$