Approche KaluzaKlein et Supersymetrie de Jauge
Abstract
This thesis presents a nonAbelian gaugesupersymmetric KaluzaKlein approach for charged spinning particles and strings in a background of gravitational and YangMills fields. In the classical KaluzaKlein approach, the basic mathematical structure is a principal bundle of which the base manifold is spacetime. This principal bundle is endowed with a pseudoRiemannian metric, invariant under the action of the structural group of the bundle, and a connection. Geodesic equations on the bundle lead to the MaxwellLorentz equation for curved spacetime and Yang Mills fields, and to a conservation law of a nonAbelian (bosonic) charge. This conservation law originates from the invariance of the freeparticle action on the bundle under the action of the structural group of the bundle (gauge group). Firstly, we generalize this approach for a spinning particle. The spin of the particle is described by Grassmannian variables added to the principal bundle. This supersymmetrization gives rise, in addition to the bosonic nonAbelian charge, a fermionic one. This leads to a search for a supergroup action on the superprincipal bundle which leaves invariant the action of the spinning particle. The invariance of this action would lead to the conservation of a nonAbelian supercharge, generalizing the conservation law obtained for particles without spin. We present Lagrangian and Hamiltonian formulations, both invariant under a super group action. The equations of motion are derived and discussed. Different terms in these equations are well known in the literature. The invariance of these formulations under a supergroup action leads to a conservation law of a nonAbelian supercharge. The bosonic part of this supercharge corresponds to the nonAbelian (bosonic) charge obtained for a particle without spin. The fermionic part is a non physical charge. It turns out in the supersymmetric case that this decouples from all other dynamical variables, and hence it does not influence trajectories of spinning particles. It is interesting to mention how this gauge supersymmetry is introduced in the dynamics. It arises by choosing the unique metric connection on the principal bundle with torsion given by the ChernSimons 3form. We then proceed to extend these formulations for spinning strings. We present Lagrangian and Hamiltonian gaugesupersymmetric formulations in a superloop space setting. The same connection corresponding to the Chern Simons 3form is used here. Equations of motion are derived and discussed. In the appendix, we discuss the effect of using this connection in a nonAbelian KaluzaKlein field theory. Using the same connection, we present a nonAbelian KaluzaKlein approach leading to a zero cosmological constant.
 Publication:

Ph.D. Thesis
 Pub Date:
 1992
 Bibcode:
 1992PhDT.......157P
 Keywords:

 FRENCH TEXT;
 Physics: Elementary Particles and High Energy; Mathematics