Scattering approach for calculating one-loop effective action and vacuum energy

TL;DR

This paper introduces a novel scattering-based approach to compute one-loop effective actions and vacuum energies in quantum field theory by transforming spectral functions from quantum mechanics methods.

Contribution

It develops a method to derive quantum field theory spectral functions from quantum mechanical scattering data, bridging the two areas.

Findings

Provides a new computational framework for effective actions and vacuum energies.

Establishes a transformation technique between quantum mechanics and quantum field theory spectral functions.

Enables calculation of quantum field spectral functions using quantum mechanical scattering data.

Abstract

We propose an approach for calculating one-loop effective actions and vacuum energies in quantum field theory. Spectral functions are functions defined by the eigenvalues of an operator. One-loop effective actions and vacuum energies in quantum field theory, as well as scattering phase shifts and scattering amplitudes in quantum mechanics, are all spectral functions. If a transformation between different spectral functions is identified, we can obtain a spectral function from another through the transformation. In this paper, we convert quantum mechanical methods for calculating scattering phase shifts and scattering amplitudes into quantum field theory methods for calculating one-loop effective actions and vacuum energies.