Renormalization for a Scalar Field in an External Scalar Potential
AbstractThe 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
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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.
Fulling SA, Settlemyre TE, Milton KA. Renormalization for a Scalar Field in an External Scalar Potential. Symmetry. 2018; 10(3):54.Chicago/Turabian Style
Fulling, Stephen A.; Settlemyre, Thomas E.; Milton, Kimball A. 2018. "Renormalization for a Scalar Field in an External Scalar Potential." Symmetry 10, no. 3: 54.
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