Research Abstract 
Within a nonequilibrium quantumfield system, such as a quarkgluon plasma (QGP) and a core of supernova explosion (SN), various processes take place, which causes spacetime evolution of the system per se. A perturbation theory for dealing with such a nonequilibrium system is a scheme, which enables one to compute reaction rates for the processes and, at the same time, to determine spacetime evolution of the system. Under the present research project, a novel perturbation theory is constructed, in which, in contrast to the conventional one, no pinch singularity appears and the Boltzmann equation, which describes spacetime evolution of the system, comes about from the theory in itself. A novel perturbation theory is framed for dealing with the nonequilibrium system that is governed by the O(N) (N=4) linearsigma model. This model describes chiral phase transition of quantum chromodynamics (QCD) that governs the QGP. The framed perturbation theory allowed one to compute various reaction rates and, simultaneously, to determine how the phase transition proceeds as a result of the reactions. A set of perturbation theories for dealing with gauge bosons, such as gluons in QCD, and fermions, such as quarks in QCD, are framed through constructing gaugeboson and fermion propagators. This theory allows one to systematically analyze nonequilibrium systems, such as those governed by a standard model (QCD, electroweak theory) and by a quantum electrodynamics (QED). As an example of the theory, rates of neutrino conversion and decay in a core region of supernova explosions. A characteristic peak structure is found for outgoing neutrino spectrum.
