Unimodular Gauge and ADM Gravity Path Integral

Abstract: This paper proposes a definition of gravitational observables and of their path integral formula within the framework of ADM foliation and the choice of unimodular gauge classes. The method enforces a BRST invariant gauge fixing of the lapse and shift fields. It yields the quantum level extension of the known classical property that the conformal classes of internal metrics of constant Lorentz time leafs define the gravitational physical degrees of freedom.