John Madore

Classical bosons in a non-commutative geometry

The classical theory of the scalar field is developed within the context of a noncommutative geometry. A non-commutative extension of Abelian gauge theory is proposed and is compared with standard non-Abelian gauge theory.

Conservation laws and integrability conditions for gravitational and Yang-Mills field equations

We show that expressed in the appropriate principal bundles, the gravitational and Yang-Mills fields equations are equivalent to integrability conditions and that the latter can also be interpreted, using local sections, as conservation equations of the local pseudo-densities of energy-momentum and Yang-Mills charge respectively. These densities can be related using a Kaluza-Klein unification.

Super matrix geometry

A generalization of a previously proposed matrix geometry is given and the theory of connections is extended to this geometry. Models constructed in the usual way from the curvature of the extended connection are shown to describe some of the features of a left-right symmetric version of the Weinberg-Salam model.

The Friedmann Universe as an Attractor of a {Kaluza-Klein} Cosmology

We show that certain cosmological models of a Kaluza-Klein theory with nonlinear Lagrangians can evolve towards the standard Friedmann universe.

On the vanishing of the cosmological constant

Abstract A lagrangian is proposed for a Kaluza-Klein theory of gravity which has a vanishing cosmological constant as stable fixed point.

A smooth oscillating cosmological solution

Abstract A metric is given, determined by the field equations derived from the Lovelock lagrangian in a Kaluza—Klein theory of gravity, whose projection onto the observable external space yields a smooth oscillating cosmological solution.