Quantization of Space-like States in Lorentz-Violating Theories

TL;DR

This paper develops a formalism to quantize Lorentz-violating theories with space-like states, enabling consistent calculations across different frames and addressing issues caused by negative-energy states.

Contribution

It introduces an extended Hamiltonian approach that allows for observer-covariant normalization and quantization of space-like states in Lorentz-violating theories.

Findings

Provides a rigorous quantization method for space-like states.

Enables calculation of Cherenkov radiation rates in any frame.

Avoids singularities in the quantization process.

Abstract

Lorentz violation frequently induces modified dispersion relations that can yield space-like states that impede the standard quantization procedures. In certain cases, an extended hamiltonian formalism can be used to define observer-covariant normalization factors for field expansions and phase space integrals. These factors extend the theory to include non-concordant frames in which there are negative-energy states. This formalism provides a rigorous way to quantize certain theories containing space-like states and allows for the consistent computation of Cherenkov radiation rates in arbitrary frames and avoids singular expressions.