Quantum States of Topologically Massive Electrodynamics and Gravity

TL;DR

This paper explicitly constructs quantum states in topologically massive electrodynamics and gravity in 2+1 dimensions, revealing infrared-regular polarization tensors with spin-dependent phases, and develops a canonical covariant quantization framework.

Contribution

It provides the first explicit realization of quantum states and algebra in these theories, including a novel regularization phase linked to spin and a comprehensive quantization approach.

Findings

Quantum states are infrared-regular with spin-dependent phases.

A canonical and covariant quantization procedure is established.

The Poincaré algebra closure is ensured by infrared finiteness.

Abstract

The free quantum states of topologically massive electrodynamics and gravity in 2+1 dimensions, are explicitly found. It is shown that in both theories the states are described by infrared-regular polarization tensors containing a regularization phase which depends on the spin. This is done by explicitly realizing the quantum algebra on a functional Hilbert space and by finding the Wightman function to define the scalar product on such a Hilbert space. The physical properties of the states are analyzed defining creation and annihilation operators. For both theories, a canonical and covariant quantization procedure is developed. The higher order derivatives in the gravitational lagrangian are treated by means of a preliminary Dirac procedure. The closure of the Poincar\'e algebra is guaranteed by the infrared-finiteness of the states which is related to the spin of the excitations through the regularization phase. Such a phase may have interesting physical consequences.