%0 Generic
%A Daus, Tristan Raphael
%C Heidelberg
%D 2025
%F heidok:37411
%R 10.11588/heidok.00037411
%T From Koopman-von Neumann to Cosmic Structure  Formation - Path Integral Approach to Classical  Many-Body Systems
%U https://archiv.ub.uni-heidelberg.de/volltextserver/37411/
%X We develop a functional integral formalism for classical many-body systems based  on the Klimontovich equation, which governs the exact evolution of the N-particle  phase-space density without loss of microscopic information. Since no assumptions  are made on the exact form of the initial state, this formalism is well suited to  describe out-of-equilibrium systems. The formalism is discussed in detail and compared to alternative approaches. Analytical solutions to the tree-level equations for homogeneous systems are presented. Importantly, a first application to cosmic large  scale structure formation is given, and numerical results are discussed. We present  one-loop results for the density fluctuation power spectrum which agree well with  results from numerical simulations and conventional approaches.