Boundary Effects in Quantum Physics

TL;DR

This paper investigates how different boundary conditions affect the vacuum energy and Casimir forces in quantum field theories, revealing a special class of boundary conditions that do not produce forces and analyzing their stability.

Contribution

It introduces a novel method to compute vacuum energy for general boundary conditions and identifies a new class of Casimirless, conformally invariant boundary conditions with implications for quantum field theory.

Findings

Identified boundary conditions that produce attractive or repulsive Casimir forces.

Discovered a family of boundary conditions that do not induce Casimir forces.

Analyzed the stability of Casimirless boundary conditions under renormalization group flow.

Abstract

We analyze the role of boundaries in the infrared behavior of quantum field theories. By means of a novel method we calculate the vacuum energy for a massless scalar field confined between two homogeneous parallel plates with the most general type of boundary properties. This allows the discrimination between boundary conditions which generate attractive or repulsive Casimir forces between the plates. In the interface between both regimes we find a very interesting family of boundary conditions which do not induce any type of Casimir force. We analyze the effect of the renormalization group flow on these boundary conditions. Even if the Casimirless conformal invariant conditions are physically unstable under renormalization group flow they emerge as a new set of conformally invariant boundary conditions which are anomaly free.