A note on the solution of a spinor equation
Tóm tắt
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.
Tài liệu tham khảo
Penrose, R., and Rindler, W. (1984).Spinors and Space-Time (Cambridge University Press, Cambridge), vol. 1.
Kalnins, E. G., McLenaghan, R. G., and Williams, G. C. (1992).Proc. Roy. Soc. Lond. 439, 103.
Walker, D. M. (1994). ‘Symmetry Operators for the Weyl-Neutrino and Maxwell's Equations on a Curved Spacetime’, M.Math. thesis, University of Waterloo.
Schlomiuk, D. (1993).Trans. Amer. Math. Soc. 338, 799.