Gauge Invariant Vacuum Polarization.
MARYLAND UNIV COLLEGE PARK CENTER FOR THEORETICAL PHYSICS
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Because of its highly singular nature, the current operator in relativistic quantum electrodynamics has to be defined by a limiting process. If gauge invariance is satisfied at every stage of this process, an additional quadratically divergent term appears in the polarizability tensor. As noted by Johnson, this new term is identical to the counter term invoked in less rigorous treatments, in order to keep the photon mass equal to zero and to satisfy gauge invariance. The author presents here an alternative derivation of Johnsons result which is based on Wards identity and which employs notions gnerally familiar to students of relativistic quantum mechanics. Author
- Quantum Theory and Relativity