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Symmetry 2018, 10(3), 54;

Renormalization for a Scalar Field in an External Scalar Potential

Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA
Department of Physics & Astronomy, Texas A&M University, College Station, TX 77843-4242, USA
H. L. Dodge Department of Physics & Astronomy, University of Oklahoma, Norman, OK 73019, USA
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Received: 31 January 2018 / Revised: 22 February 2018 / Accepted: 22 February 2018 / Published: 27 February 2018
(This article belongs to the Special Issue Casimir Physics and Applications)
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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. View Full-Text
Keywords: vacuum energy; renormalization; Pauli–Villars; point splitting; boundary; potential; scalar field vacuum energy; renormalization; Pauli–Villars; point splitting; boundary; potential; scalar field
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Fulling, S.A.; Settlemyre, T.E.; Milton, K.A. Renormalization for a Scalar Field in an External Scalar Potential. Symmetry 2018, 10, 54.

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