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

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.

arXiv commentNew version published in PRD, Lee-Wick prescription in Sec. IV-C, 27 pages, 5 figures

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• Higher order derivatives extension of Maxwell-Chern-Simons electrodynamics in the presence of field sources and material boundaries
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• Tree-level unitarity, causality and higher-order Lorentz and CPT violation
• A Two-Gauge Field Model for Magnetoelectric Boundaries
• Ghosts in higher derivative Maxwell-Chern-Simon's theory and $\mathcal{P}\mathcal{T}-$symmetry
• Emission Distribution for the quantas of Maxwell-Chern-Simon Gauge Field coupled to External Current
• Extended Chern-Simons model for a vector multiplet
• Higher-derivative $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetric Maxwell-Chern-Simons theories at one loop in superspace