Causality, unitarity, and indefinite metric in Maxwell-Chern-Simons extensions

TL;DR

This paper investigates the quantization of (2+1)-dimensional electrodynamics with a higher-derivative Chern-Simons term, analyzing causality and unitarity issues, and demonstrating that the Lee-Wick prescription preserves these properties at one-loop order.

Contribution

It provides a canonical quantization framework for Maxwell-Chern-Simons extensions with higher derivatives, addressing unitarity and causality concerns with the Lee-Wick prescription.

Findings

Microcausality is preserved with the Lee-Wick prescription.

Perturbative unitarity holds up to one-loop order.

The theory includes a standard photon and a massive ghost degree of freedom.

Abstract

We canonically quantize $(2+1)$-dimensional electrodynamics including a higher-derivative Chern-Simons term. The effective theory describes a standard photon and an additional degree of freedom associated with a massive ghost. We find the Hamiltonian and the algebra satisfied by the field operators. The theory is characterized by an indefinite metric in the Hilbert space that brings up questions on causality and unitarity. We study both of the latter fundamental properties and show that microcausality as well as perturbative unitarity up to one-loop order are conserved when the Lee-Wick prescription is employed.