Orthogonal gauge fixing of first order gravity

Understand

We consider the first order connection formulation of 4D general relativity in the "orthogonal" gauge.

• We show how the partial gauge fixing of the phase space canonical coordinates leads to the appearance of second class constraints in the theory.
• We employ the gauge unfixing procedure in order to successfully complete the Dirac treatment of the system.
• While equivalent to the inversion of the Dirac matrix, the gauge unfixing allows us to work directly with the reduced phase space and the ordinary Poisson bracket.