Abstract
A survey is given of the structure and applications of spinor fields in three-dimensional (pseudo-) Riemannian manifolds. A systematic treatment, independent of the metric signature, is possible since there exists a fairly general structure, to be associated with unitary spinors, which encompasses all but the reality properties. The discussion begins with the algebraic and analytic properties of unitary spinors, the Ricci identities and curvature spinor, followed by the spinor adjungation as space reflection, and the SU(2) and SU(l,l) spin coefficients with some applications. The rapidly increasing range of applications includes space-times with Killing symmetries, the initial-value formulation, positivity theorems on gravitational energy and topologically massive gauge theories.
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