Spacetime foam

TL;DR

This paper models spacetime foam using scalar fields on flat spacetime, proposing a path integral approach that accounts for all topologies and introduces a natural cutoff, with implications for quantum gravity.

Contribution

It introduces a novel path integral formulation for spacetime foam that incorporates all topologies without free parameters, impacting quantum gravity research.

Findings

Path integral accounts for all spacetime topologies.

The cutoff is determined by the field theory itself.

New features of Feynman diagrams are outlined.

Abstract

Spacetime foam is analyzed within the simplistic model of a set of scalar fields on a flat background. We suggest the formula for the path integral which allows to account for the all possible topologies of spacetime. We show that the proper path integral defines a cutoff for the field theory. The form of the cutoff is fixed by the field theory itself and has no free additional parameters. New features of the Feynman diagram technic are outlined and possible applications in quantum gravity are discussed.