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Point Splitting and U(1) Gauge Invariance

Dirk Olivie
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Abstract

A gauge transformation in quantum electrodynamics involves the product of field operators at the same space-time point and hence does not have a well-defined meaning. One way to avoid this difficulty is to generalize the gauge transformation by using different space-time points in the spirit of Dirac's point splitting. Such a generalization indeed exists and the resulting infinitesimal gauge transformation takes the form of an infinite series in the coupling constant. In this text I will present two examples of generalized gauge transformations.

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Dirk Olivie. 1999-12-20. Point Splitting and U(1) Gauge Invariance. https://arxiv.org/abs/hep-th/9912178

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