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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics and quantum mechanics, a Dirac operator is a differential operator that is a formal square root, or half-iterate, of a second-order operator such as a Laplacian. The original case which concerned Paul Dirac was to factorise formally an operator for Minkowski space, to get a form of quantum theory compatible with special relativity; to get the relevant Laplacian as a product of first-order operators he introduced spinors.This is a special case of the Atiyah-Singer-Dirac operator acting on sections of a spinor bundle.