Ultraviolet divergences, renormalization and nonlocality of interactions in quantum field theory

TL;DR

This paper explores how renormalization in quantum field theory leads to nonlocal interactions and presents a generalized dynamical equation that renders the theory ultraviolet-finite.

Contribution

It demonstrates that renormalized local quantum field theories can be reformulated with nonlocal interactions via a generalized dynamical equation, ensuring ultraviolet finiteness.

Findings

Renormalization induces nonlocal interactions in quantum field theories.

A generalized dynamical equation can describe the renormalized theory.

The reformulation achieves ultraviolet finiteness of the theory.

Abstract

We discuss the dynamical situation which arises in a local quantum field theory after renormalization. By using the example of the three-dimensional theory of a neutral scalar field interacting through the quartic coupling, we show that after renormalization the dynamics of a theory is governed by a generalized dynamical equation with a nonlocal interaction operator. It is shown that the generalized dynamical equation allows one to formulate this theory in an ultraviolet-finite way.