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.

arXiv comment29 pages; v2 minor corrections and references added, to appear in EPJC

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Cited by in corpus (7)

• Ultraviolet-complete quantum field theories with fractional operators
• Slavnov-Taylor identities, non-commutative gauge theories and infrared divergences
• Muon $g-2$ anomaly and non-locality
• BPHZ renormalization and its application to non-commutative field theory
• Aspects of perturbative quantum field theory on non-commutative spaces
• Noncommutative Gauge Theories: Model for Hodge theory
• Gauge Fields on Non-Commutative Spaces and Renormalization