Stability, Causality, and Lorentz and CPT Violation

TL;DR

This paper examines the stability and causality of quantum field theories with Lorentz and CPT violation, showing that issues arise at high energies unless the theory is derived from a nonlocal, spontaneous symmetry-breaking framework.

Contribution

It provides explicit calculations demonstrating stability and causality conditions in Lorentz and CPT violating theories, supporting their consistency within a string theory context.

Findings

Low-energy stability and causality are maintained with small Lorentz/CPT violation parameters.

High-energy violations of positivity or microcausality can occur unless the theory is nonlocal.

Spontaneous Lorentz and CPT violation from a nonlocal theory can preserve stability and causality.

Abstract

Stability and causality are investigated for quantum field theories incorporating Lorentz and CPT violation. Explicit calculations in the quadratic sector of a general renormalizable lagrangian for a massive fermion reveal that no difficulty arises for low energies if the parameters controlling the breaking are small, but for high energies either energy positivity or microcausality is violated in some observer frame. However, this can be avoided if the lagrangian is the sub-Planck limit of a nonlocal theory with spontaneous Lorentz and CPT violation. Our analysis supports the stability and causality of the Lorentz- and CPT-violating standard-model extension that would emerge at low energies from spontaneous breaking in a realistic string theory.