Gravitational quantum states as finite representations of the Lorentz group

Abstract

A manifestly Lorentz-covariant formulation of loop quantum gravity (LQG) is given in terms of finite-dimensional representations of the Lorentz group. The formulation accounts for discrete symmetries, such as parity and time-reversal, and it establishes a link with Wigner classification of particles. The resulting quantum model can be seen as LQG-like with the internal SU(2) ⊗ SU(2) group and it is free of the Immirzi parameter, while the scalar constraint is just the Euclidean part.