GT4 - Inertial Forces, Optical Metrics and Particle Motion Properties |
Speaker_ |
Carminati, John |
Co-autors |
A. E. K. Lim |
Talk _ |
The determination of all syzygies for the dependent polynomial invariants of the Riemann tensor. II: Mixed invariants of even degree in the Ricci spinor |
Abstract _ |
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 Ö_{ABAB} and show how, using constructive graph-theoretic methods, arbitrary scalar contractions between copies of the Weyl spinor Ø_{ABCD}, its conjugate Ø_{ABCD} 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. |