Nonperturbative Lorentz Violation and Field Quantization

TL;DR

This paper explores nonperturbative regimes of Lorentz-violating effective field theories, demonstrating that standard quantization methods can be applied, but identifying a ground state requires additional physical criteria beyond the free theory.

Contribution

It shows that conventional quantization methods remain valid in certain nonperturbative Lorentz-violating theories, highlighting the need for extra physical input to define the ground state.

Findings

Quantization methods are applicable in nonperturbative Lorentz-violating regimes.

Absence of observer-invariant energy positivity complicates ground state identification.

Thermodynamics may play a role in understanding these theories.

Abstract

Regimes of Lorentz-violating effective field theories are studied in which departures from Lorentz symmetry are nonperturbative. Within a free toy theory exhibiting Lorentz breakdown involving an operator of mass dimension three, it is shown that conventional methods suffice to achieve field quantization and Fock-space construction. However, the absence of an observer-invariant energy-positivity condition requires physical input beyond the free theory for the unambiguous identification of a ground state. An investigation of the role of thermodynamics in this context is instigated.