arXiv subjects
Publications and source records attributed to Yuichi Mizutani.
An Abelian gauge theory with Chern-Simons term is investigated for a four-component Dirac fermion in 1+2 dimensions. The Ball-Chiu (BC) vertex function is employed to modify the rainbow-ladder approximation for the Schwinger-Dyson (SD) equation. We numerically solve the SD equation and show the gauge dependence for the resulting phase boundary for the parity and the chiral symmetry.
Relativistic quantum field theories for complex scalar and Dirac fields are investigated in non-equilibrium thermo field dynamics. The thermal vacuum is defined by the Bogoliubov transformed creation and annihilation operators. Two independent Bogoliubov parameters are introduced for a charged field. Its difference naturally induces the chemical potential. Time-dependent thermal Bogoliubov transformation generates the thermal counter terms. We fix the terms by the self-consistency renormalization condition. Evaluating the thermal self-energy under the self-consistency renormalization condition, we derive the quantum Boltzmann equations for the relativistic fields.
A relativistic neutral scalar field is investigated in non-equilibrium thermo field dynamics. The canonical quantization is applied to the fields out of equilibrium. Because the thermal Bogoliubov transformation becomes time-dependent, the equations of motion for the ordinary unperturbed creation and annihilation operators are modified. This forces us to introduce a thermal counter term in the interaction Hamiltonian which generates additional radiative corrections. Imposing the self-consistency renormalization condition on the total radiative corrections, we obtain the quantum Boltzmann equation for the relativistic scalar field.
A relativistic neutral scalar field is investigated on the basis of the Schwinger-Dyson equation in the non-equilibrium thermo field dynamics. A time evolution equation for a distribution function is obtained from a diagonalization condition for the Schwinger-Dyson equation. An explicit expression of the time evolution equation is calculated in the $λϕ^4$ interaction model at the 2-loop level. The Boltzmann equation is derived for the relativistic scalar field. We set a simple initial condition and numerically solve the Boltzmann equation and show the time evolution of the distribution function and the relaxation time.