Functional evolution of scalar fields in bounded one-dimensional regions

TL;DR

This paper investigates the unitarity of quantum evolution for a 1+1 dimensional free scalar field in a bounded region under various boundary conditions, ensuring consistent quantum dynamics.

Contribution

It analyzes the unitarity of quantum evolution in bounded regions with different boundary conditions, extending understanding of quantum field behavior in confined geometries.

Findings

Unitarity holds for certain boundary conditions.

Boundary conditions significantly affect quantum evolution.

The study clarifies conditions for consistent quantum dynamics in bounded regions.

Abstract

We discuss the unitarity of the quantum evolution between arbitrary Cauchy surfaces of a 1+1 dimensional free scalar field defined on a bounded spatial region and subject to several types of boundary conditions including Dirichlet, Neumann and Robin.