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arXiv · 1802.02883

Renormalization for a Scalar Field in an External Scalar Potential

S. A. Fulling·T. E. Settlemyre·K. A. Milton
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Abstract

The Pauli--Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential are isolated into a three-parameter local, covariant functional of the background potential. These divergences can be naturally absorbed into coupling constants of the potential, regarded as a dynamical object in its own right; here this is demonstrated in detail for two different models of the field-potential coupling. here is a residual dependence on the logarithm of the potential, reminiscent of the renormalization group in fully interacting quantum field theories; these terms are finite but numerically dependent on an arbitrary mass or length parameter, which is purely a matter of convention. This work is one step in a program to elucidate boundary divergences by replacing a sharp boundary by a steeply rising smooth potential.

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S. A. Fulling, T. E. Settlemyre, K. A. Milton. 2018-02-05. Renormalization for a Scalar Field in an External Scalar Potential. https://doi.org/10.3390/sym10030054

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