Null hypersurface initial data for classical fields of arbitrary spin and for general relativity

Details Null hypersurface initial data for classical fields of arbitrary spin and for general relativity Null hypersurface initial data for classical fields of arbitrary spin and for general relativity

Mar 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980gregr..12..225p&link_type=abstract

General Relativity and Gravitation, vol. 12, Mar. 1980, p. 225-264. USAF-NSF-supported research.

Physics

48

Astronomical Models, Boundary Value Problems, Field Theory (Physics), Hyperspaces, Null Zones, Relativity, Maxwell Equation, Set Theory, Spinor Groups

Scientific paper

Consideration is given to the use of spinors and null hypersurfaces in place of the usual space-like hypersurfaces on which to specify initial data in an initial value problem in the theory of interacting fields in relativity. It is noted that the approach presented has an advantage over the more usual Cauchy problem in that all constraints are eliminated from the theory in both special and general relativity. The two-component spinor calculus involved in the approach is introduced, and a general scheme for interacting fields which describes all fields in terms of sets of irreducible spinors is presented. It is shown that the concept of an exact set of such spinors is appropriate for an initial value problem on a null cone without constraints, with initial data expressed in the form of a complex number, the null datum, defined at each point of the null cone and corresponding to one spinor. It is noted that the approach presented as applied to a general exact set is incomplete in that it depends on the null data being analytic and the initial hypersurface being a cone; however these restrictions can be removed in the case of basic free fields, including the Weyl neutrino field, the free Maxwell field and the linearized gravitational field.

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