## 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.

Original language | English |
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Pages (from-to) | 205-210 |

Number of pages | 6 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 523 |

Issue number | 1-2 |

DOIs | |

State | Published - 20 Dec 2001 |

### Bibliographical note

Funding 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.).