Negative-frequency modes in quantum field theory

TL;DR

This paper explores a modified quantum field theory allowing negative-energy momentum eigenstates, which cancels divergences and zero-point energy, while maintaining causality and consistency with electroweak corrections.

Contribution

It introduces a novel quantum field theory framework with negative-frequency modes, addressing divergence issues and aligning with standard electroweak results.

Findings

Cancels ultra-violet divergences

Eliminates zero-point energy

Maintains causality and consistency with electroweak corrections

Abstract

We consider a departure from standard quantum field theory, constructed so as to permit momentum eigenstates of both positive and negative energy. The resulting theory is intriguing because it brings about the cancellation of leading ultra-violet divergences and the absence of a zero-point energy. The theory gives rise to tree-level source-to-source transition amplitudes that are manifestly causal and consistent with standard S-matrix elements. It also leads to the usual result for the oblique corrections to the standard electroweak theory. Remarkably, the latter agreement relies on the breakdown of naive perturbation theory due to resonance effects. It remains to be shown that there are no problems with perturbative unitarity.