https://doi.org/10.1140/epjc/s10052-012-2262-0
Regular Article - Theoretical Physics
On the renormalization of non-commutative field theories
1
Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria
2
Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040, Vienna, Austria
3
Institut de Physique Nucléaire, Bat. P. Dirac, Université de Lyon, Université Lyon 1 and CNRS/IN2P3, 4 rue Enrico Fermi, 69622, Villeurbanne, France
4
Austro-Ukrainian Institute for Science and Technology, c/o TU Vienna, Wiedner Hauptstraße 8-10, 1040, Vienna, Austria
* e-mail: daniel.blaschke@univie.ac.at
Received:
5
September
2012
Revised:
29
November
2012
Published online:
15
January
2013
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 Z c [j] of connected Green functions makes sense (at least at one-loop level). 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: Explicit computations are performed at one-loop order and the generalization to higher loops is commented upon. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization.
© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica, 2013