Quantum Fields bounded by one dimensional crystal plates

TL;DR

This paper investigates how boundary conditions affect a massless scalar quantum field confined between two one-dimensional crystal plates, analyzing spectral properties and Casimir energy implications.

Contribution

It classifies all regular boundary conditions consistent with unitarity and characterizes the spectral function for this quantum field setup.

Findings

Classified all regular boundary conditions for the scalar field.

Computed the spectral function for different boundary conditions.

Linked spectral properties to Casimir energy calculations.

Abstract

We get deeper understanding of the role played by boundary conditions in quantum field theory, by studying the structure of a scalar massless quantum field theory bounded by two one dimensional planar crystal plates. The system can also be understood as a massless scalar confined to propagate in the surface of a finite cylinder. We classify the most general type of regular behaved boundary conditions that the quantum field can satisfy, in accordance with the unitarity principle of quantum field theory. Also, we characterize the frequency spectrum for each quantum field theory, by computing the holomorphic spectral function. The spectral function is the starting point to compute the Casimir energy as a global function over the space of allowed boundary conditions for the quantum field theory.