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.
|Number of pages
|Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
|Published - 20 Dec 2001
Bibliographical noteFunding Information:
This work was supported in part by the BK21 project of the Ministry of Education, Korea, and also by Korea Research Foundation Grant 2001-015-DP0085 (C.L.).