Some boundary effects in quantum field theory

TL;DR

This paper develops a quantum field theory in a finite box with periodic boundary conditions, deriving an expression for the effective coupling constant that depends on the box size, highlighting boundary effects in quantum fields.

Contribution

It introduces a novel construction of quantum field theory in finite volumes using harmonic oscillators on a circle, explicitly deriving the effective coupling's dependence on box size.

Findings

Effective coupling constant depends explicitly on the box dimension

Boundary effects influence quantum field interactions

Framework can be used to study finite-volume quantum phenomena

Abstract

We have constructed a quantum field theory in a finite box, with periodic boundary conditions, using the hypothesis that particles living in a finite box are created and/or annihilated by the creation and/or annihilation operators, respectively, of a quantum harmonic oscillator on a circle. An expression for the effective coupling constant is obtained showing explicitly its dependence on the dimension of the box.