New Approach to Transport Theory in Classical Gases

A new approach to transport theory in classical gases is described for a hard-sphere gas. The approach is designed to incorporate collective effects (sound waves, mean free path) at an early stage. A pseudopotential approximation to the $N$-body Liouville equation is given. By working only with symmetric distribution functions, a simple analogy to a quantum-mechanical many-body Hamiltonian is possible. The linearized Boltzmann equation is obtained as the "Hartree" solution to the single-particle states of this Hamiltonian. Sound waves appear as long-wavelength "single-particle" excitations. Collective excitations include the excluded volume correction to the velocity of sound. The "single-particle" solutions have the advantage of introducing the appropriate long-range space-time correlations into the basis functions for higher-order approximations. Because of the pseudopotential approximation in the present paper, there are short-range divergences in higher orders of perturbation theory, but no apparent long-wavelength divergences.