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Boltzmann Equation for Relativistic Neutral Scalar Field in Non-equilibrium Thermo Field Dynamics

A relativistic neutral scalar field is investigated on the basis of the Schwinger-Dyson equation in the non-equilibrium thermo field dynamics. A time evolution equation for a distribution function is obtained from a diagonalization condition for the Schwinger-Dyson equation. An explicit expression of the time evolution equation is calculated in the $λϕ^4$ interaction model at the 2-loop level. The Boltzmann equation is derived for the relativistic scalar field. We set a simple initial condition and numerically solve the Boltzmann equation and show the time evolution of the distribution function and the relaxation time.

preprint2011arXivOpen access
Yuichi MizutaniTomohiro Inagaki
hep-th
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Yuichi MizutaniTomohiro Inagaki

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