The action and the physical scale of field theory

TL;DR

This paper develops a geometric, evolution-based approach to field theory that introduces a universal physical scale, relates it to observable cosmological parameters, and challenges traditional notions of physical dimensionality and regularization.

Contribution

It proposes an axiomatic, geometry-driven formulation of field theory using evolution equations and a universal scale, providing finite, nonlocal effective actions at all orders.

Findings

The universal physical scale is linked to the Hubble constant.

The covariant effective action remains finite at all orders.

Higher-order actions generalize classical gravity and gauge theories.

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.