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2012

On the Renormalization of Non-Commutative Field Theories

Blaschke, Daniel N., Garschall, Thomas, Gieres, Francois et al.

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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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D. N. Blaschke, F. Gieres, E. Kronberger, M. Schweda and M. Wohlgenannt,
Original
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