Symmetry operators for Dirac's equation on two-dimensional spin manifolds

TL;DR

This paper explores how symmetry operators for the Dirac equation in two-dimensional spin manifolds can be characterized using geometric objects like Killing vectors and tensors, impacting separation of variables.

Contribution

It demonstrates that second order symmetry operators are expressible via Killing vectors and tensors, linking geometric symmetries to Dirac equation solutions.

Findings

Symmetry operators are expressed in terms of Killing vectors and tensors.

The role of these operators in separation of variables is analyzed.

Provides a geometric framework for understanding Dirac symmetries.

Abstract

It is shown that the second order symmetry operators for the Dirac equation on a general two-dimensional spin manifold may be expressed in terms of Killing vectors and valence two Killing tensors. The role of these operators in the theory of separation of variables for the Dirac equation is studied.