Ghosts in higher derivative Maxwell-Chern-Simon's theory and $\mathcal{PT}-$symmetry

TL;DR

This paper investigates the $ ext{PT}$-symmetry in higher derivative Maxwell-Chern-Simons theory, addressing ghost issues by using second class constraints to mitigate instabilities, revealing conditions among operator coefficients.

Contribution

It explores the $ ext{PT}$-symmetric properties of extended Maxwell-Chern-Simons theory and demonstrates how second class constraints influence ghost removal and stability conditions.

Findings

Partial removal of ghost instabilities using second class constraints.

Conditions among operator coefficients are derived for stability.

$ ext{PT}$-symmetry plays a role in the ghost dynamics.

Abstract

Ghost fields in quantum field theory have been a long-standing problem. Specifically, theories with higher derivatives involve ghosts that appear in the Hamiltonian in the form of linear momenta term, which is commonly known as the Ostrogradski ghost. Higher derivative theories may involve both types of constraints i.e. first class and second class. Interestingly, these higher derivative theories may have non-Hermitian Hamiltonian respecting $\mathcal{PT}-$symmetries. In this paper, we have considered the $\mathcal{PT}-$symmetric nature of the extended Maxwell-Chern-Simon's theory and employed the second class constraints to remove the linear momenta terms causing the instabilities. We found that the removal is not complete rather conditions arise among the coefficients of the operator ${Q}$.