The Time Surface Term in Quantum Gravity

Abstract

The role of the time surface term in the ADM Hamiltonian formulation of general relativity is investigated. We show that the variable contained in the time surface term (the scale factor) plays the role of a time-like variable. The conjugated variable represents the energy density in the reduced phase space, where the Schrödinger like equation for a wave function is derived. The contribution from the surface term to the phase of the wave function allows us to define {\bf the phase time of the quantum Universe} so that it coincides with {\bf the proper time as an invariant interval} for the classical dust filled Universe. The quantum scenario of the evolution of the Universe filled in by the Weinberg-Salam fields is considered. The wave function of the early Universe as the functional from the Higgs fields and scale factor realizes the unitary irreducible representation of the SO(4,1) group. The elementary particle masses are determined by the angles of the scale--scalar field mixing.