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The determination of all syzygies for the dependent polynomial invariants of the Riemann Tensor. II. mixed invariants of Eeven degree in the Ricci Spinor

journal contribution
posted on 2006-05-01, 00:00 authored by John Carminati, Allan Lim
We continue our analysis of the polynomial invariants of the Riemann tensor in a four-dimensional Lorentzian space. We concentrate on the mixed invariants of even degree in the Ricci spinor ΦABȦḂ and show how, using constructive graph-theoretic methods, arbitrary scalar contractions between copies of the Weyl spinor ψABCD, its conjugate ψȦḂĊḊ and an even number of Ricci spinors can be expressed in terms of paired contractions between these spinors. This leads to an algorithm for the explicit expression of dependent invariants as polynomials of members of the complete set. Finally, we rigorously prove that the complete set as given by Sneddon [J. Math. Phys. 39, 1659-1679 (1998)] for this case is both complete and minimal.

History

Journal

Journal of mathematical physics

Volume

47

Issue

5

Pagination

1 - 24

Publisher

American Institute of Physics

Location

New York, N. Y.

ISSN

0022-2488

eISSN

1089-7658

Language

eng

Publication classification

C1 Refereed article in a scholarly journal; C Journal article

Copyright notice

2006, American Institute of Physics

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