Quantum States of Topologically Massive Electrodynamics and Gravity

Details Quantum States of Topologically Massive Electrodynamics and Gravity Quantum States of Topologically Massive Electrodynamics and Gravity

1996-02-22

arxiv.org/abs/hep-th/9602127v1

J.Phys.A29:3179-3198,1996

Physics

High Energy Physics

High Energy Physics - Theory

21 page, latex, no figures

Scientific paper

10.1088/0305-4470/29/12/022

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.

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