Note on stability and microcausality in Lorentz violating antisymmetric tensor field

TL;DR

This paper investigates microcausality and energy positivity in Lorentz-violating antisymmetric tensor and vector field theories, revealing differences in their fundamental consistency conditions.

Contribution

It compares two classically equivalent theories, showing that they differ in satisfying microcausality and energy positivity under Lorentz violation.

Findings

Antisymmetric tensor theory satisfies energy positivity.

Tensor theory can satisfy microcausality with specific vacuum choices.

Vector theory violates both conditions under Lorentz violation.

Abstract

The fundamental issues of microcausality and energy positivity conditions are important to be investigated in the context of spontaneous Lorentz violating theories. We check the microcausality and energy positivity conditions for a free rank-2 antisymmetric tensor field with spontaneous Lorentz violating term and a classically equivalent vector theory from dispersion relations and propagators, and find that the two theories lead to different conditions. While the antisymmetric tensor theory satisfies energy positivity condition and can satisfy microcausality condition for a particular choice of vacuum value, the vector theory violates both energy positivity and microcausality conditions.