One-loop Effective Actions in Shape-invariant Scalar Backgrounds
arXiv:hep-th/0110154 · doi:10.1016/S0370-2693(01)01312-0
Abstract
The field-theoretic one-loop effective action in a static scalar background depending nontrivially on a single spatial coordinate is related, in the proper-time formalism, to the trace of the evolution kernel (or heat kernel) for an appropriate, one dimensional, quantum-mechanical Hamiltonian. We describe a recursive procedure applicable to these traces for shape-invariant Hamiltonians, resolving subtleties from the continuum mode contributions by utilizing the expression for the regularized Witten index. For some cases which include those of domain-wall-type scalar backgrounds, our recursive procedure yields the full expression for the scalar or fermion one-loop effective action in both (1+1) and (3+1)-dimensions.
11 pages, LaTeX2e