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In this paper we study equations of state of Casimir vacuum of massive scalar field and massive bispinor field in compact Friedmann universe. With use of the Abel–Plana formula the renormalization of divergent series for calculation of the quantum means of operators is implemented. [ABSTRACT FROM AUTHOR]

The global time in geometrodynamics is defined in a covariant under diffeomorphisms form. An arbitrary static background metric is taken in the tangent space. The global intrinsic time is identified with the mean value of the logarithm of the square root of the ratio of the metric determinants. The procedures of the Hamiltonian reduction and deparametrization of dynamical systems are implemented. The reduced Hamiltonian equations of motion of gravitational field in semi-geodesic coordinate system are written. [ABSTRACT FROM AUTHOR]

The quantum Casimir condensate of a conformal massive scalar field in a compact Friedmann universe is considered in the static approximation. The Abel–Plana formula is used for renormalization of divergent series in the condensate calculation. A differential relation between the static Casimir energy density and static Casimir condensate is derived. [ABSTRACT FROM AUTHOR]