Date of Award

10-1-1989

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Physics & Astrophysics

Abstract

A smooth (1:2) tensor field A on a finite dimensional Banach space E is used to define a derivation, called the A-derivative and analogous to the covariant derivative of General Relativity, on the algebra of smooth tensor fields on E. The A-derivative is only an $\IR$-multilinear map into the ring C(E) of all smooth $\IR$-valued functions on E and thus the field equation, which is simply the requirement that the A-derivative of A vanish, is thus covariant under automorphisms of the base space E. The curvature and torsion tensors of the A-derivation are defined once again by analogy to the curvature and torsion tensors of a linear connection and any smooth (1:2) tensor field on E is said to be a dynamical connection if (a) its A-derivative with respect to itself and (b) it is flat, that is the curvature tensor is zero. The class of dynamical connections are studied in detail.

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