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.

Wigner$apos$s little group as a gauge generator in linearized gravity theories

“…with β = k k 0 and γ = k 0 |µ| . Identical results were obtained in other contexts [18] by different methods. Here, we have shown how these results can be obtained in a simpler and straightforward manner just by considering the momentum space expression of the equation of motion in the rest frame using the plane wave method with a subsequent boost transformation.…”

“…We can therefore study the gauge transformation generated in this doublet. The polarization vector for L ± , with only one degree of freedom for each of L + and L − , has been found to be [10,18] εa…”

Hamiltonian Analysis for Abelian and Non-Abelian Massive Theories in Three Dimensions

“…These theories were introduced as generalizations of three-dimensional Chern-Simons actions or in other cases, can also be considered as a zero coupling limit of Yang-Mills [YM] theories [3,4]. The importance for studying topological actions has been motived in several contexts of theoretical physics given that have a closed relation with physical theories, for instance it is wellknow that from the Chern-Simons topological action arises a topological mass when it is added to actions just as electrodynamics or gravity in three dimensions [5,6]; at quantum level an infrared cut-off cures the infrared problem without disturbing the ultraviolet or gauge properties of those theories. On the other hand, in [7] it is reported an analysis of specific limits in the gauge coupling of topological theories yielding a pure YM dynamics in four and three dimensions.…”