Abstract
We examine the noncommutative counterpart of QED, called as noncommutative QED (NC-QED). The minimal coupling to U(1) gauge field compatible with the ∗-product admits the matter with only three varieties of charges, i.e., 0, +1 and −1. Ultraviolet divergence can be removed by multiplicative renormalization of classical action at one loop level. The infrared aspect of the theory is first examined by calculating the anomalous magnetic dipole moment. The dependence on the direction of photon momentum reflects the Lorentz symmetry violation of the present system. The finite part of the photon vacuum polarization shows the infrared singularity like ln( q· C T C· q) ( C μν is a noncommutative parameter.) which also exists in noncommutative Yang-Mills theory. It is associated with the ultraviolet behavior of the theory. We also consider the extension to chiral gauge theory in the present context, but the requirement of anomaly cancellation allows only NC-QED.
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