The paper is devoted to the description a measurable time-interval (``proper time'') in the Hamiltonian version of general relativity with the Dirac-ADM metric. To separate the dynamical parameter of evolution from the space metric we use the Lichnerowicz conformally invariant variables. In terms of these variables GR is equivalent to the conformally invariant Penrose-Chernicov-Tagirov theory of a scalar field the role of which is played by the scale factor multiplied on the Planck constant. Identification of this scalar field with the modulus of the Higgs field in the standard model of electroweak and strong interactions allows us to formulate an example of conformally invariant unified theory where the vacuum averaging of the scalar field is determined by cosmological integrals of motion of the Universe evolution.Comment: 20 pages, latex, no figures, submited to General Relativity and Garvitatio

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The reparametrization-invariant generating functional for the unitary and causal perturbation theory in general relativity in a finite space-time is obtained. The region of validity of the Faddeev-Popov-DeWitt functional is studied. It is shown that the invariant content of general relativity as a constrained system can be covered by two "equivalent" unconstrained systems: the "dynamic" (with "dynamic" evolution parameter as the metric scale factor) and "geometric" (given by the Levi-Civita type canonical transformation to the action-angle variables where the energy constraint converts into a new momentum)."Big Bang," the Hubble evolution, and creation of matter fields by the "geometric" vacuum are described by the inverted Levi-Civita transformation of the geomeric system into the dynamic one. The particular case of the Levi-Civita transformations are the Bogoliubov ones of the particle variables (diagonalizing the dynamic Hamiltonian) to the quasiparticles (diagonalizing the equations of motion). The choice of initial conditions for the "Big Bang" in the form of the Bogoliubov (squeezed) vacuum reproduces all stages of the evolution of the Friedmann-Robertson-Walker universe in their conformal (Hoyle-Narlikar) versions. PACS numbers: 04.60.-m, 04.20.Cv, 98.80.Hw (Quantum Gravity) GR Equivalent Unconstrained system Faraday FIELD Newton PARTICLE VARIATION SYMMETRY Fig. 1. The tree of modern theoretical physics grew from two different roots ("particle" and "field") which gave the VARIATIONAL method and SYMMETRY principles for formulating modern physical theories as constrained systems. To obtain unambiguous physical results, one should construct equivalent unconstrained systems compatible with the simplest variational method. It is just the problem discussed in the present paper. Int. J. Mod. Phys. A 2001.16:1715-1742. Downloaded from www.worldscientific.com by WESTERN MICHIGAN UNIVERSITY on 02/04/15. For personal use only. STATEMENT OF PROBLEM FADDEEV-POPOV INTEGRAL RENORMA-LIZABILITY BIG BANG

The unification of general relativity and standard model for strong and electroweak interactions is considered on the base of the conformal symmetry principle. The Penrose-Chernikov-Tagirov Lagrangian is used to describe the Higgs scalar field modulus and gravitation. We show that the procedure of the Hamiltonian reduction converts the homogeneous part of the Higgs field into the dynamical parameter of evolution of the equivalent reduced system. The equation of dynamics of the "proper time" of an observer with respect to the evolution parameter reproduces the Friedmann-like equation, which reflects the cosmological evolution of elementary particle masses. The value of the Higgs field is determined, at the present time, by the values of mean density of matter and the Hubble parameter in satisfactory agreement with the data of cosmological observations.

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