The action and the physical scale of field theory

Abstract

The evolution equation is used as the fundamental equation of field theory, which is described entirely by the geometry of the four-dimensional space. The evolution kernel determines the covariant action of physical fields by the proper time integral. This axiomatic definition introduces into dimensionless theory the universal physical scale (characteristic length). The universal scale relates the action's geometrical orders expressed in the field strength tensors. The covariant effective action is finite at any order in the curvatures and nonlocal starting from the second order. Its two lowest, local orders correspond to the cosmological constant term and the gravity action. The action of gauge fields appears in the second order term. The higher, nonlocal orders generalize the classical actions of gravity and gauge fields. The characteristic length is determined by the measured Hubble constant. The Planck scale values have no physical significance. The physical dimensionality is violated in functional integration. The dimensional regularization is an ill-defined procedure.