Relativistic quantum transport theory approach to multiparticle production

Abstract

The field-theoretic description of multiparticle production processes is cast in a form analogous to ordinary transport theory. Inclusive differential cross sections are shown to be given by integrals of covariant phasespace distributions. The single-particle distribution function $F(p,R)$ is defined as the Fourier transform of a suitable correlation function in analogy with the nonrelativistic (Wigner) phase-space distribution function. Its transform $F(p,q)$ is observed to be essentially the discontinuity of a multiparticle scattering amplitude. External-field problems are studied to exhibit the physical content of the formalism. When $q=0\mathrm{}$ one recovers the single-particle distribution exactly. The equation of motion for $F(p,R)$ generates an infinite hierarchy of coupled equations for various distribution functions. In the Hartree approximation one obtains nonlinear integral equations analogous to the Vlasov equation in plasma physics. Such equations are convenient for exhibiting collective motions; in particular it appears that a collective mode exists in a ${\phi }^4$ theory for a uniform infinite medium. It is speculated that such collective modes could provide a theoretical basis for clustering effects in multiparticle production.