Non-Equilibrium Quantum Field Theory and Entangled Commutation Relations

Non-equilibrium quantum field theory studies time dependence of processes which are not available for the S-matrix description. One of the new methods of investigation in non-equilibrium quantum theory is the stochastic limit method. This method is an extension of the works by Bogoliubov, van Hove and Prigogine and it permits to study not only the system but also the reservoir degrees of freedom. We consider the stochastic limit of translation invariant Hamiltonians in quantum field theory and show that the master field satisfies a new type of commutation relations, the so called entangled (or interacting) commutation relations. These relations extend the interacting Fock relations established earlier in non-relativistic QED and the free (or Boltzmann) commutation relations which have been found in the large N limit of QCD. As an application of the stochastic limit method we consider the photon splitting cascades in magnetic field and show that photons in cascades form entangled states ("triphons") and they obey not Bose but a new type of statistics corresponding to the entangled commutation relations.