Dirichlet boundary conditions in a noncommutative theory

TL;DR

This paper explores how to impose boundary conditions in a noncommutative quantum field theory, analyzing their physical implications, symmetry preservation, and effects on observables like Casimir energies.

Contribution

It introduces a method to implement Dirichlet-like boundary conditions in a noncommutative setting and examines their impact on physical observables and symmetries.

Findings

Boundary conditions can be effectively imposed in noncommutative theories.

Imposing boundary conditions affects Casimir energy calculations.

Certain symmetries are preserved despite boundary modifications.

Abstract

We study the problem of imposing Dirichlet-like boundary conditions along a static spatial curve, in a planar Noncommutative Quantum Field Theory model. After constructing interaction terms that impose the boundary conditions, we discuss their implementation at the level of an interacting theory, with a focus on their physical consequences, and the symmetries they preserve. We also derive the effect they have on certain observables, like the Casimir energies.