Showing papers on "Ricci decomposition published in 1975"

On the decomposition of tensor products of principal series representations for real-rank one semisimple groups

Abstract: Let G be a connected semisimple real-rank one Lie group with finite center. It is shown that the decomposition of the tensor product of two representations from the principal series of G consists of two pieces, Tc and Td, where Tc is a continuous direct sum with respect to Plancherel measure on G of representations from the principal series only, occurring with explicitly determined multiplicities, and Td is a discrete sum of representations from the discrete series of G, occurring with multiplicities which are, for the present, undetermined.

Tensor operators and the trace metric

Abstract: The traditional unit tensor operators are shown to be orthonormal vectors in a trace metric approach. The operator equivalents of crystal field theory are used as models of the tensor operators which act as generators in Lie group theory.

Some properties of asymptotically flat, static, Einstein−Maxwell space−times

Abstract: We show that the generators of the Weyl tensor for asymptotically flat, static, Einstein−Maxwell space−times are electric type to asymptotic order r−7 and that for space−times which are stable under static perturbations the generators of the electromagnetic field tensor are electric type to order r−5. We also argue that the Weyl tensor, the Ricci tensor, and the electromagnetic field tensor may fail to be electric type in general for asymptotically flat, static, Einstein−Maxwell space−times but that the generators of the Weyl tensor and the electromagnetic field tensor may still be electric type in general. The variable r is an affine parameter along null geodesics.

Elucidation of some of lanczos' thoughts concerning spacetime curvature and the local and non-local parts of the riemann tensor

Abstract: The central role of the Riemann curvature tensor in Einstein's gravitational theory, including the significance of its invariant decomposition in spacetime (with respect to the duality and trace operations) into essentially local and non-local parts, is considered in the light of some of the thoughts and contributions of Cornelius Lanczos (1893–1974). Also, in this context, the fundamental role of the embedded two-space elements, specified by simple bivectors, in defining the Riemannian curvatures is briefly investigated. In particular, it is shown that the formulation of a bivector form of geodesic deviation for the Riemannian curvatures elucidates some of the insights of Weyl and Lanczos. Finally, some of Lanczos' thoughts relating to the nature of the essentially local and non-local parts of the Riemann tensor are discussed. These considerations are discussed in terms of Lanczos' discovery (1962) of the existence (in all Riemannian spacetimes) of a third order tensor Hijkthat can be regarded as the potential of the non-local (Weyl) part of the Riemann tensor.

The electromagnetic field as a Finsler manifold

Abstract: We elucidate the possibility of treating the electromagnetic field consistently as a Finsler manifold with the metric calculated in explicit form. The curvature tensor of the unified gravielectromagnetic field is studied. It is shown that its contraction gives the correct Lagrangian density.