Field theory in form calculus

Cartan's calculus gained acceptance more and more by its obvious elegant and economic calculation technique, as well as by the development of new differential geometrical methods, as e.g. fibre bundle techniques in gauge theory, which contain exterior forms as geometrical/physical objects. The thesis at issue provides a thorough-going, consequent application of the calculus of exterior forms to the most important topics in (classical) field theory, as for instance to the general Lagrangian and Hamiltonian formulation, or to gauge theories, in particular to gauge theoretical models of gravitation. The particular reformulation of gauge theory in terms of exterior forms offers a straightforward application to the 4-dimensional translation group T(4). The inclusion of the spin aspect by gauging also the Lorentz group SO(3,1) leads to a field theory over a Riemann/Cartan space-time (with or without propagating torsion). In a general gauge theory of gravity of this sort, based on T(4)xSO(3,1) as the underlying gauge group, torsion forms play the role of Lorentz covariant translational field strengths, and the Riemann/Cartan curvature forms correspond to the Lorentz field strengths. Modern developments in gauge theory, demand for a fibre bundle version also. Hence, in addition a detailed treatment of G-manifold, G-fibre bundles and principal G-fibre bundles with connection is given with a particular accentuation of Cartan's calculus over the bundle space. (Author)