Quantum States of Topologically Massive Electrodynamics and Gravity

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 Poincaré 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.

21 page, latex, no figures

References in corpus (4)

• The Projective Unitary Irreducible Representations of the Poincaré Group in 1+2 Dimensions
• The Spectrum of Topologically Massive Quantum Electrodynamics
• Canonical Quantization of the Maxwell-Chern-Simons Theory in the Coulomb Gauge
• Constrained Analysis of Topologically Massive Gravity

Cited by in corpus (2)

• Wigner's little group as a gauge generator in linearized gravity theories
• Hamiltonian analysis for abelian and non-abelian massive theories in three dimensions