Generalized Gravity I : Kinematical Setting and reformalizing Quantum Field Theory

TL;DR

This paper develops a differential calculus on non-commutative manifolds, extends fundamental principles like covariance, and introduces a new, causal, covariant formulation of quantum field theory surpassing traditional methods.

Contribution

It introduces a natural differential calculus on non-commutative manifolds and a novel, manifestly causal and covariant quantum field theory formulation.

Findings

Extended covariance and equivalence principles lead to gauge theory emergence.

A new causal, covariant quantum field theory formulation is proposed.

Representation of the theory on a kinematical structure is provided.

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.