arXiv subjects
Publications and source records attributed to Theo Verwimp.
With the help of Weil polynomials on the Lie algebra of the Poincaré group in D dimensions, we construct a Lagrangian form for higher dimensional gravity on a principal fibre bundle whose base space is an even-dimensional Riemann-Cartan spacetime and whose structure group is the Poincaré group.
The Glashow-Weinberg-Salam gauge field Lagrangian for electroweak theory and the Townsend-Zardecki action for gravitation are obtained from the same type of Yang-Mills Weil form on a principal fiber bundle over space-time, with symmetry group U(2) and SO(2,3), respectively. The unified geometrical approach given here shows that fiber bundle reduction and symmetry breaking are essential not only in electroweak theory but also in the SO(2,3) gauge theory for gravitation. In fact, the process of symmetry breaking in electroweak theory and the soldering of the anti-de Sitter bundle, essential in the interpretation of SO(2,3) gauge theory as a theory for gravitation, are corresponding geometrical concepts.
By dimensional reduction of the Lovelock Lagrangian, effective four-dimensional field equations and expressions for the cosmological and gravitational constants are obtained. A cosmological model is discussed with the n-torus as internal space.
Boundary terms for Lovelock gravity are obtained by calculating in arbitrary dimension the index theorem for the de Rham complex of a manifold with nonempty boundary.
The Lovelock Lagrangian is for even dimension D obtained from Weil polynomials on the Lie algebra of the Lorentz group SO(1,D-1). The procedure for generating it is related to the Weil homomorphism that converts Lie algebra invariants into cohomology classes.
First a review is given of Riemann-Cartan space-time and Einstein-Cartan gravity. This gives us the necessary tools to handle the SO(2,3) Yang-Mills gauge theory for gravity. Field equations are obtained from a Yang-Mills gauge field Lagrangian. From these field equations and the Bianchi identities the conservation laws for anti-de Sitter theory are derived. Possible solutions of the field equations are discussed. The only solution found for a RW-geometry with a perfect fluid matter content is the early universe. There are no Schwarzschild solutions of the torsion free vacuum field equations if curvature squared terms cannot be neglected.