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

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.