Microcausality and quantization of the fermionic Myers-Pospelov model

TL;DR

This paper investigates the fermionic Myers-Pospelov model, analyzing its different background cases, quantizing the timelike case, and examining microcausality violations caused by higher time derivatives.

Contribution

It provides a detailed analysis of the fermionic sector of the Myers-Pospelov model across various backgrounds, identifying physical consistency conditions and quantizing the timelike case.

Findings

Spacelike case is well-defined with explicit Lorentz violation.

Lightlike case is ill-defined and discarded.

Timelike case is physically consistent with new modes and microcausality violations near the light cone.

Abstract

We study the fermionic sector of the Myers and Pospelov theory with a general background $n$. The spacelike case without temporal component is well defined and no new ingredients came about, apart from the explicit Lorentz invariance violation. The lightlike case is ill defined and physically discarded. However, the other case where a nonvanishing temporal component of the background is present, the theory is physically consistent. We show that new modes appear as a consequence of higher time derivatives. We quantize the timelike theory and calculate the microcausality violation which turns out to occur near the light cone.