Effective action for a free scalar field in the presence of spacetime foam

TL;DR

This paper models spacetime foam as a gas of virtual wormholes and derives an effective Lagrangian for a free scalar field that includes non-local interactions, revealing insights into particle-wormhole interactions and regularization.

Contribution

It introduces a novel effective Lagrangian for scalar fields in spacetime foam, capturing non-local effects and particle-wormhole interactions, including a self-interaction mechanism.

Findings

Reproduces Pauli-Villars regularization via wormhole scattering

Derives a self-interaction term from back reaction effects

Provides a framework for scalar field behavior in quantum foam

Abstract

We model spacetime foam by a gas of virtual wormholes. For a free scalar field we derive the effective Lagrangian which accounts for the interaction with spacetime foam and contains two additional non-local terms. One term describes the scattering of scalar particles on virtual wormholes and explicitly reproduces the Pauli-Villars regularization procedure. The second term describes the back reaction of particles on the number density of wormholes and introduces a self-interaction between particles.