Quantum field theory with an interaction on the boundary

TL;DR

This paper studies quantum field theories with boundary interactions, revealing that boundary effects alter the scaling behavior of fields, potentially reducing singularities compared to bulk interactions.

Contribution

It introduces a framework for analyzing quantum fields with boundary interactions and demonstrates altered scaling properties on the boundary.

Findings

Boundary interactions lead to different scaling behaviors on the brane.

Quantum theories with boundary interactions can be less singular than purely bulk theories.

Scaling properties depend on the dimensionality of the boundary and bulk.

Abstract

We consider quantum theory of fields \phi defined on a D dimensional manifold (bulk) with an interaction V(\phi) concentrated on a d<D dimensional surface (brane). Such a quantum field theory can be less singular than the one in d dimensions with the interaction $V(\phi)$. It is shown that scaling properties of fields on the brane are different from the ones in the bulk.