Adiabatic Switching-Off of Interactions and Foundations of the Boltzmann Equation

Abstract

The Boltzmann equation for a monatomic gas is derived with the aid of the adiabatic switching-off interactions, starting with the Heisenberg equation of motion for a number operator in phase space introduced by Ono. It is shown that neither Kirkwood's time-averaging procedure nor the random phase approximation is necessary by virtue of the switching-off of interactions and a new method of time-differentiation. The effectiveness of the present formalism is demonstrated in an analysis of higher order interactions, and the Boltzmann equation is corrected so as to include multiple scattering effects.