Renormalization for a Scalar Field in an External Scalar Potential. (arXiv:1802.02883v1 [hep-th])
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.