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Abstract

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.