Vacuum Energy of a Non-relativistic String with Nontrivial Boundary Condition

TL;DR

This paper calculates the vacuum energy of a non-relativistic quantum string with free-sliding ends on angled rods, revealing a sum of Luscher potential and an angle-dependent term.

Contribution

It derives the partition function and vacuum energy for a non-relativistic string with nontrivial boundary conditions using path integral methods.

Findings

Vacuum energy includes Luscher potential plus angle-dependent term

Classical solutions for the string with angled boundary conditions derived

Partition function obtained via path integral method

Abstract

We derive the partition function of a non-relativistic quantum string which its ends are allowed to freely slide on the two angled straight solid rods. We first derive the classical solution of the model and then use it to derive the partition function utilizing the path integral method. We show that the vacuum energy is sum of the Luscher potential plus a term which depends on the relative angle between rods.