A note on the solution of a spinor equation

Details A note on the solution of a spinor equation A note on the solution of a spinor equation

Sep 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995gregr..27..973c&link_type=abstract

General Relativity and Gravitation, Volume 27, Issue 9, pp.973-979

Physics

Scientific paper

An equation of spinor algebra, which is specified by two positive integers,M andN, is solved by relating it to the problem of integrating a two-dimensional Hamiltonian homogeneous polynomial system of ordinary differential equations, whose degree isN}-1. The case in whichN=1 reduces to a well-known result of spinor algebra. The caseM=N=4 is of relevance in the study of symmetry operators of Maxwell's equations on a curved space-time. It is also shown, using spinor notation, that the first integral for a general two-dimensional Hamiltonian system of ordinary differential equations (whether polynomial or analytic) is determinable in a purely algebraic manner, i.e., by using no integration.

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