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The Boltzmann Equation in Classical and Quantum Field Theory

Sangyong Jeon
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Abstract

Improving upon the previous treatment by Mueller and Son, we derive the Boltzmann equation that results from a classical scalar field theory. This is obtained by starting from the corresponding quantum field theory and taking the classical limit with particular emphasis on the path integral and perturbation theory. A previously overlooked Van-Vleck determinant is shown to control the tadpole type of self-energy that can still appear in the classical perturbation theory. Further comments on the validity of the approximations and possible applications are also given.

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Sangyong Jeon. 2005-07-18. The Boltzmann Equation in Classical and Quantum Field Theory. https://doi.org/10.1103/physrevc.72.014907

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