Gauge Invariance and Integration Rules

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Abstract
The Feynman-Dyson rules of integration for the scattering matrix elements in perturbation expansion have long been known to lead to gauge-variant results in the case of certain closed loop diagrams. It is shown that a more careful integration which avoids unjustified interchanges of integrations and limiting processes keeps the theory gauge-invariant throughout, without the need of explicit cutoffs or appeal to invariance for the specification of undefined integrals. The Feynman-Dyson rules can thus easily be amended to assure gauge invariance.

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