Renormalization for a Scalar Field in an External Scalar Potential

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 functiona...

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Bibliographic Details
Published in:Symmetry (Basel) 2018-03, Vol.10 (3), p.54
Main Authors: Fulling, Stephen, Settlemyre, Thomas, Milton, Kimball
Format: Article
Language:English
Subjects:
boundary
Coupling
Mathematical models
Parameters
Pauli–Villars
point splitting
potential
Quantum theory
Regularization
renormalization
scalar field
vacuum energy
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Summary: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. There 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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym10030054