On the Renormalization of Non-Commutative Field Theories
Abstract
This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space). To start with, we discuss the Quantum Action Principle and provide evidence for its validity for non-commutative quantum field theories by showing that the equation of motion considered as insertion in the generating functional Zc[j] of connected Green functions makes sense. Second, we consider the generalization of the BPHZ renormalization scheme to non-commutative field theories and apply it to the case of a self-interacting real scalar field. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization.
Keywords
Cite
@article{arxiv.1207.5494,
title = {On the Renormalization of Non-Commutative Field Theories},
author = {Daniel N. Blaschke and Thomas Garschall and Francois Gieres and Franz Heindl and Manfred Schweda and Michael Wohlgenannt},
journal= {arXiv preprint arXiv:1207.5494},
year = {2013}
}
Comments
29 pages; v2 minor corrections and references added, to appear in EPJC