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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 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.
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http://hal.in2p3.fr/in2p3-00840087
Contributor : Dominique Girod <>
Submitted on : Monday, July 1, 2013 - 2:59:42 PM
Last modification on : Tuesday, November 19, 2019 - 2:38:06 AM

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D.N. Blaschke, T. Garschall, F. Gieres, F. Heindl, M. Schweda, et al.. On the renormalization of non-commutative field theories. European Physical Journal C: Particles and Fields, Springer Verlag (Germany), 2013, 73, pp.2262. ⟨10.1140/epjc/s10052-012-2262-0⟩. ⟨in2p3-00840087⟩

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