Generalized Gravity I : Kinematical Setting and reformalizing Quantum Field Theory

Abstract

The first part of this work deals with the development of a natural differential calculus on non-commutative manifolds. The second part extends the covariance and equivalence principle as well studies its kinematical consequences such as the arising of gauge theory. Furthermore, a manifestly causal and covariant formulation of quantum field theory is presented which surpasses the usual Hamiltonian and path integral construction. A particular representation of this theory on the kinematical structure developed in section three is moreover given.