Euler-Heisenberg lagrangian through Krein regularization

TL;DR

This paper derives the Euler-Heisenberg effective action in Krein space quantization, providing a convergent, renormalization-free solution that matches the traditional renormalized result for a constant electromagnetic field.

Contribution

It introduces a novel approach using Krein space quantization to obtain the Euler-Heisenberg action without renormalization, aligning with established results.

Findings

Convergent, renormalization-free effective action derived

Matches the traditional renormalized Euler-Heisenberg action

Demonstrates the viability of Krein space quantization in quantum field theory

Abstract

The Euler-Heisenberg effective action at the one-loop for a constant electromagnetic field is derived in Krein space quantization with Ford's idea of uctuated light-cone. In this work we present a perturbative, but convergent solution of the effective action. Without using any renormalization procedure, the result coincides with the famous renormalized Euler-Heisenberg action.