Ghosts in higher derivative Maxwell-Chern-Simon's theory and [formula omitted]-symmetry

Biswajit Paul,Himangshu Dhar,Biswajit Saha

doi:10.1016/j.physletb.2020.135671

Biswajit Paul, Himangshu Dhar + Show 1 more

Open Access

https://doi.org/10.1016/j.physletb.2020.135671

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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 PT-symmetries. In this paper, we have considered the 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.

Highlights

We know from usual quantum mechanics that for real energy eigenvalues of a quantum theory, it is required that we must have a Hermitian Hamiltonian i.e. H = H†
There is only one primary first class constraints Φ20 which indicates existence of one gauge symmetry. This higher derivative MCS Lagrangian is invariant under the transformations ξ1′ μ → ξ1μ + ∂μλ, where λ is arbitrary parameter indicating that the theory has a underlying symmetry of U (1) group
Imk(k5 8c kmk5 8c ǫij kmsk5 8c ǫij. It is clear from the above expression of the Hamiltonian (53) that all the terms are square powers of the respective fields and there is no term involving any linear momenta

Summary

INTRODUCTION

For a non-Hermitian Hamiltonian, if it has unbroken PT −symmetry the energy spectrum of the theory can be real This means, more systems which were earlier outright thought to have complex eigen values due to lack of Hermiticity, can be added and analysed to have real eigen values. According to the Ostrodradski method, in HD theories, velocities of the fields are considered as independent fileds and the Hamiltonian poses linear momenta conjugate to these fields This is very unusual for the theories where the equation of motion is mostly second order in time [33].

MAXWELL CHERN SIMON’S MODEL

PT TRANSFORMATION OF FIELD VARIABLES

SIMILARITY TRANSFORMATIONS OF THE CANONICAL HAMILTONIAN OWING TO PT

CONCLUSION