QUANTUM STATES OF TOPOLOGICALLY MASSIVE ELECTRODYNAMICS AND GRAVITY

The free quantum states of topologically massive electrodynamics and g ravity in 2+1 dimensions are found explicitly. It is shown that in bot h theories the states are described by infrared-regular polarization t ensors containing a regularization phase which depends on the spin. Th is is done by explicitly realizing the quantum algebra on a functional Hilbert space and by finding the Wightman function to define the scal ar product on such a Hilbert space. The physical properties of the sta tes are analysed defining creation and annihilation operators. For bot h theories, a canonical and covariant quantization procedure is develo ped. The higher-order derivatives in the gravitational Lagrangian are treated by means of a preliminary Dirac procedure. The closure of the Poincare algebra is guaranteed by the infrared-finiteness of the state s which is related to the spin of the excitations through the regulari zation phase. Such a phase may have interesting physical consequences.