# Self-adjointness of two-dimensional Dirac operators on domains

## TL;DR

This paper proves the self-adjointness of two-dimensional Dirac operators on planar domains under various boundary conditions, ensuring their mathematical well-posedness in quantum mechanics models.

## Contribution

It provides a direct proof of self-adjointness for Dirac operators on planar domains with broad boundary conditions, advancing mathematical understanding in quantum physics.

## Key findings

- Self-adjointness established for a large class of boundary conditions
- Proof applicable in Sobolev space $H^1$
- Enhances mathematical foundation for quantum models

## Abstract

We consider Dirac operators defined on planar domains. For a large class of boundary conditions, we give a direct proof of their self-adjointness in the Sobolev space $H^1$.