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Noncommutative Regularization In Gauge Theories

Katsusada Morita
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Abstract

Gauge invariance of noncommutative (NC) regularization which, on the basis of a Lorentz-invariant NC action regarded as a `regulated' action, neither introduces auxiliary fields nor extends dimensions to complex values, is proved by explicitly calculating photon self-energy in the one-loop approximation in scalar QED. Transversality of vacuum polarization in NC regularization is also briefly reviewed comparing with Pauli-Villars-Gupta and dimensional regularizations. NC regularization is applied to gauge-invariant calculation of one-loop gluon self-energy in U(N) gauge theory. It is shown that U(1) decouples from SU(N) in the one-loop gluon self-energy diagrams. That is, gauge-invariant result on the one-loop SU(N) gluon self-energy is obtained from consideration of Lorentz-invariant NC U(N) gauge theory.

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Katsusada Morita. 2004-04-05. Noncommutative Regularization In Gauge Theories. https://arxiv.org/abs/hep-th/0404038

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