On the formal developments in kinetic theory I : The exact master equations

Abstract

A summary of the main equations and formulae of the Brussels formalism (including the asymptotic theory, the ΩΨ-operator, the transformation theory and the redefined initial condition) is provided and discussed with the aid of formal techniques avoiding duplications of the proofs for homogeneous and inhomogeneous systems and stressing the mathematical structure. Applications to Lorentz transformations of the asymptotic master equations and to the formal collision operator are also discussed. This first part is devoted to the derivation of the exact master equations and a discussion of their basic properties.