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Abstract

The method of 'covariant perturbation theory' allowed for the computation of
the kernel of the evolution equation on a spin Riemannian manifold. The
proposed axiomatic definition of the effective action introduces the universal
scale parameter, with the length square dimensionality, into a dimensionless
mathematical theory. It is shown that this geometrical result has a physical
meaning of the action of field theory, including gravity. Two orders lowest in
a tensor rank in this functional are independent of a spin group and local.
They reproduce the action of relativity with the cosmological constant. The
modern value of the universal scale could be determined by the measured Hubble
constant. The variable scale parameter could let us build axiomatic
cosmological theories.