Some Considerations Regarding Lorentz-Violating Theories

TL;DR

This paper examines the compatibility of Lorentz-violating quantum field theories with causality and stability, suggesting that such theories can be consistent at low energies if they originate from a nonlocal, Lorentz-violating string theory framework.

Contribution

It proposes that Lorentz-violating theories are viable low-energy limits of nonlocal string-inspired models with spontaneous Lorentz breaking.

Findings

Low-energy Lorentz violation can be compatible with causality and stability.

High-energy Lorentz violation may lead to causality or positivity violations.

Spontaneous Lorentz violation from nonlocal theories can resolve high-energy issues.

Abstract

We investigate the compatibility of Lorentz-violating quantum field theories with the requirements of causality and stability. A general renormalizable model for free massive fermions indicates that these requirements are satisfied at low energies provided the couplings controlling the breaking are small. However, for high energies either microcausality or energy positivity or both are violated in some observer frame. We find evidence that this difficulty can be avoided if the model is interpreted as a sub-Planckian approximation originating from a nonlocal theory with spontaneous Lorentz violation. The present study thereby supports the validity of the standard-model extension as the low-energy limit of any realistic string theory that exhibits spontaneous Lorentz breaking.