Quantum field theory without divergences

TL;DR

This paper proposes a method to eliminate divergences in quantum field theory by incorporating measurement resolution into the definition of fields, resulting in finite Green functions, demonstrated with Euclidean -field theory.

Contribution

It introduces a novel approach that modifies quantum fields based on measurement resolution, removing the need for traditional renormalization procedures.

Findings

Green functions become finite when measurement resolution is incorporated.

The approach successfully applied to Euclidean -field theory.

Divergences are linked to unphysical, unmeasurable quantities.

Abstract

It is shown that loop divergences emerging in the Green functions in quantum field theory originate from correspondence of the Green functions to {\em unmeasurable} (and hence unphysical) quantities. This is because no physical quantity can be measured in a point, but in a region, the size of which is constrained by the resolution of measuring equipment. The incorporation of the resolution into the definition of quantum fields $\phi(x)\to\phi^{(A)}(x)$ and appropriate change of Feynman rules results in finite values of the Green functions. The Euclidean $\phi^4$-field theory is taken as an example.