## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- Conference on Mathematical Relativity. Robert Bartnik, ed. Proceedings of the Centre for Mathematical Analysis, v. 19. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1989), 207 - 221

### Unitary spinor methods in general relativity

#### 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.

#### Article information

**Dates**

First available in Project Euclid:
18 November 2014

**Permanent link to this document**

https://projecteuclid.org/
euclid.pcma/1416335853

**Mathematical Reviews number (MathSciNet)**

MR1020801

**Zentralblatt MATH identifier**

0684.53018

#### Citation

Perjés, Zoltán. Unitary spinor methods in general relativity. Conference on Mathematical Relativity, 207--221, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1989. https://projecteuclid.org/euclid.pcma/1416335853