Semiclassical Energy Levels of Sine-Gordon Model on a Strip with Dirichlet Boundary Conditions

TL;DR

This paper derives explicit semiclassical energy levels for the Sine-Gordon model on a finite strip with Dirichlet boundaries, providing formulas for vacuum and kink states and analyzing their limits.

Contribution

It presents the first analytic expressions for semiclassical energy levels of the Sine-Gordon model with boundary conditions in a finite geometry.

Findings

Explicit formulas for vacuum and kink energy levels

Analysis of ultraviolet and infrared limits

Solutions of Lame' type Schrödinger equations

Abstract

We derive analytic expressions of the semiclassical energy levels of Sine-Gordon model in a strip geometry with Dirichlet boundary condition at both edges. They are obtained by initially selecting the classical backgrounds relative to the vacuum or to the kink sectors, and then solving the Schodinger equations (of Lame' type) associated to the stability condition. Explicit formulas are presented for the classical solutions of both the vacuum and kink states and for the energy levels at arbitrary values of the size of the system. Their ultraviolet and infrared limits are also discussed.