The Dirac operator on a Riemannian manifold with a spin structure is the first-order differential
operator obtained by composing the spinor covariant
derivative with Clifford multiplication. In a local orthonormal frame it is 
. Its square
is related to the connection Laplacian and scalar curvature by the Lichnerowicz formula
involving the scalar curvature.
Dirac Operator
See also
Clifford Algebra, Differential Operator, SpinorExplore with Wolfram|Alpha
References
Lawson, H. B. Jr. and Michelsohn, M.-L. Spin Geometry. Princeton, NJ: Princeton University Press, 1989.Cite this as:
Weisstein, Eric W. "Dirac Operator." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DiracOperator.html