In a framework describing manifestly covariant relativistic evolution using a scalar time τ, consistency demands that τ-dependent fields be used. In recent work by the authors, general features of a classical parametrized theory of gravitation, paralleling general relativity where possible, were outlined. The existence of a preferred “time” coordinate τ changes the theory significantly. In particular, the Hamiltonian constraint for τ is removed From the Euler-Lagrange equations. Instead of the 5-dimensional stress-energy tensor, a tensor comprised of 4-momentum density mid flux (...) density only serves as the source. Building on that foundation, in this paper we develop a linear approximate theory of parametrized gravitation in the spirit of the flat spacetime approach to general relativity. Using a modified form of Kraichnan's flat spacetime derivation of general relativity, we extend the linear theory to a family of nonlinear theories in which the flat metric and the gravitational field coalesce into a single effective curved metric. (shrink)

We investigate a theory in which fundamental objects are branes described in terms of higher grade coordinates $X^{\mu{_1}\ldots \mu{_n}}$ encoding both the motion of a brane as a whole, and its volume evolution. We thus formulate a dynamics which generalizes the dynamics of the usual branes. Geometrically, coordinates $X^{\mu{_1} \ldots \mu{_n}}$ and associated coordinate frame fields { ${\gamma_{\mu{_1}\ldots\mu{_n}}}$ } extend the notion of geometry from spacetime to that of an enlarged space, called Clifford space or C-space. If we start from (...) four-dimensional spacetime, then the dimension of C-space is 16. The fact that C-space has more than four dimensions suggests that it could serve as a realization of Kaluza-Klein idea. The “extra dimensions” are not just the ordinary extra dimensions, they are related to the volume degrees of freedom, therefore they are physical, and need not be compactified. Gauge fields are due to the metric of Clifford space. It turns out that amongst the latter gauge fields there also exist higher grade, antisymmetric fields of the Kalb–Ramond type, and their non-Abelian generalization. All those fields are naturally coupled to the generalized branes, whose dynamics is given by a generalized Howe–Tucker action in curved C-space. (shrink)