Dirac-like operators on the Hilbert space of differential forms on manifolds with boundaries

TL;DR

This paper investigates self-adjoint extensions of Dirac-type operators on manifolds with boundaries, including irregular boundaries and point-like interactions, providing explicit boundary conditions for two-dimensional cases.

Contribution

It offers a comprehensive analysis of self-adjoint boundary conditions for Dirac operators on manifolds with various boundary types, including explicit results for two-dimensional manifolds.

Findings

Explicit self-adjoint boundary conditions for 2D manifolds

Analysis of boundary conditions for regular and irregular boundaries

Inclusion of point-like interactions in higher dimensions

Abstract

The problem of self-adjoint extensions of Dirac-type operators in manifolds with boundaries is analysed. The boundaries might be regular or non-regular. The latter situation includes point-like interactions, also called delta-like potentials, in manifolds of dimension higher than one. Self-adjoint boundary conditions for the case of dimension 2 are obtained explicitly.