# Dirac operator

From Diffgeom

*This article defines a property that can be evaluated for a differential operator on a differential manifold (viz a linear map from the space of differentiable functions to itself)*

## Definition

### Given data

Let be a Riemannian manifold and a vector bundle over . Let denote a (the?) Laplacian on .

### Definition part

A **Dirac operator** on is a differential operator from the sheaf of section of to itself, whose square is .

In other words, a Dirac operator is a formal squareroot, or a half-iterate, of the Laplacian.