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Journal Articles European Physical Journal C: Particles and Fields Year : 2013

On the renormalization of non-commutative field theories

D.N. Blaschke
  • Function : Author
T. Garschall
  • Function : Author
F. Heindl
  • Function : Author
M. Schweda
  • Function : Author
M. Wohlgenannt
  • Function : Author

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.

Dates and versions

in2p3-00840087 , version 1 (01-07-2013)

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Cite

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, 2013, 73, pp.2262. ⟨10.1140/epjc/s10052-012-2262-0⟩. ⟨in2p3-00840087⟩
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