On the physical interpretation of effective actions using Schwinger's formula

TL;DR

This paper demonstrates that Schwinger's formula for one-loop effective actions can be physically interpreted as summing the zero-point energies of quantum fields, confirmed through formal proof and regularization.

Contribution

It provides a clear physical interpretation of Schwinger's formula as summing zero-point energies, supported by formal proof and regularization methods.

Findings

Schwinger's formula corresponds to zero-point energy summation.

The interpretation is validated through formal proof.

Regularization confirms the physical meaning.

Abstract

We show explicitly that Schwinger's formula for one-loop effective actions corresponds to the summation of energies associated with the zero-point oscillations of the fields. We begin with a formal proof, and after that we confirm it using a regularization prescription.