Kinetic Field Theory: a new formalism for microscopic perturbation theory

Abstract

This thesis provides a general construction of the Kinetic Field Theory (KFT) framework and its microscopic perturbation theory for any classical physical system which can be described by a Hamiltonian. The generating functional of KFT is constructed based on a definition of phase space in terms of the cotangent bundle of configuration space and utilizing methods borrowed from the path integral formulation of classical mechanics. From it, observables of the system and their expectation values are derived. In order to facilitate calculations, an expansion in the interactions is performed leading to a microscopic perturbation theory. Improvements over previous approaches to this perturbative treatment include novel expressions for contributions to observables as well as a transparent diagrammatic formalism, both in a significantly generalized setting. The results are applied to two problems from the field of cosmology: cosmic structure formation and clustering of cosmic neutrinos.