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arXiv · 1207.5494

On the Renormalization of Non-Commutative Field Theories

Daniel N. Blaschke·Thomas Garschall·Francois Gieres·Franz Heindl·Manfred Schweda·Michael Wohlgenannt
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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.

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Daniel N. Blaschke, Thomas Garschall, Francois Gieres, Franz Heindl, Manfred Schweda, Michael Wohlgenannt. 2013-01-08. On the Renormalization of Non-Commutative Field Theories. https://doi.org/10.1140/epjc%2Fs10052-012-2262-0

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