Relativistic transport theory of fluctuating fields for hadrons

We analyze the physics of relativistic nuclear collisions and demonstrate that an adequate treatment of pions must include the quantum time-energy uncertainty principle and nonsequential three-body collisions. We apply relativistic quantum field theory to obtain exact equations determining the time evolution of hadronic fields and their fluctuations in terms of the effective interactions describing scattering in matter. These equations relate the main physical observables to the sought-after properties of nuclear matter, and involve only these quantities and the corresponding properties of free-space one- and two-body processes. We show how to regularize the singularities by employing the internal structure of the mesons, while maintaining causality and unitarity. We show that, in a very good approximation, the dynamic quantities reduce to functions of eight variables---those of the Boltzmann equation, supplemented by the energy of the hadron. Our method appears capable of deducing the properties of hot dense nuclear matter from data already measured in experiments on the collisions of heavy nuclei.