Boost invariant regulator for field theories

TL;DR

This paper explores the limitations of relativistic cutoffs in field theories, proposing a combined approach with point splitting and amplitude suppression to achieve stable dynamics and novel vacuum structures.

Contribution

It introduces a new regulator method combining point splitting with amplitude suppression to address stability issues in relativistic field theories.

Findings

Relativistic cutoffs are mostly incompatible with non-perturbative regulation.

Point splitting combined with amplitude suppression can stabilize semiclassical dynamics.

A new vacuum structure emerges from the proposed regulation method.

Abstract

It is shown that by imposing the relativistic symmetries on the cutoff in field theories one rules out all known non-perturbative regulators except the point splitting. The relativistic cutoff dynamics is non-local in time and thereby unstable, bringing the very existence of relativistic field theory into question. It is argued within the context of a scalar field theory model that the combination of the point splitting with a sufficiently fast suppression in the field amplitude may lead to stable semiclassical dynamics and to a new kind of realistic vacuum structure.