Hidekazu Tanaka

We extend the Schwinger–Dyson equation (SDE) on the complex plane, which was treated in our previous research, to finite temperature. As a simple example, we solve the SDE for a model with four-fermion interactions in (1+1) space-time dimensions in the strong coupling region. We investigate the properties of the effective mass and energy for the fermions, especially near the phase transition temperature.

Effective mass and energy are investigated using the Schwinger-Dyson equation (SDE) in the complex plane. As simple examples, we solve the SDE for the (1+1)-dimensional model and the strongly coupled quantum electrodynamics (QED). We also study some properties of the effective mass and energy in the complex plane.

We investigate the properties of quark mass functions in quantum chromodynamics calculated by the Schwinger–Dyson equation in the strong coupling region, in which the loop integration is performed in Minkowski space. The calculated results are compared with those obtained by integration in Euclidean space.

Three-body decay functions in space-like parton branches are implemented to evaluate transverse-momentum-dependent (TMD) parton distribution functions in the next-to-leading logarithmic (NLL) order of quantum chromodynamics (QCD). Interference contributions due to the next-to-leading-order terms are taken into account for the evaluation of the transverse momenta in initial state parton radiations. Some properties of the decay functions are also examined.

We formulate new two dimensional fermions breaking $\gamma_{5}$hermiticity, based on the minimal doubling fermion. We investigate their properties: (I) Symmetries, (II) eigenvalue distributions, and (III)the number of poles. As a simple application of the fermions, the Gross-Neveu model in two dimensions is studied using the fermion. We obtain the parity broken phase diagram called Aoki phase and the chiral broken phase diagram of the model with an imaginary chemical potential.

We construct 2D non-γ₅ hermiticity fermions based on the minimal doubling fermion. We investigate symmetries, reflection positivity, eigenvalue distribution, and the number of poles for our fermions. As simple tests for its application to the fermion, the Gross–Neveu model in two dimensions is studied using the non-γ₅ hermiticity fermion. We show the parity broken phase diagram, called the Aoki phase, and the chiral broken phase diagram for the model with an imaginary chemical potential.

We construct 2D non-$\gamma_{5}$hermiticity fermions based on the minimal doubling fermion. We investigate symmetries, reflection positivity, eigenvalue distribution and the number of poles for our fermions. As simple tests for application to the fermion, the Gross-Neveu model in two dimensions is studied using the non-$\gamma_{5}$hermiticity fermion. We draw the parity broken phase diagram, called Aoki phase and the chiral broken phase diagram for the model with an imaginary chemical potential.

We analyze the lattice fermion kinetic term using PT symmetry, R-hermiticity, and $\gamma_{5}$-hermiticity. R-hermiticity is a condition for Hermite action and it is related to $\gamma_{5}$-hermiticity and PT symmetry. Assuming that a translation-invariant kinetic term with continuum and periodic function does not have PT symmetry, it can have R-hermiticity or $\gamma_{5}$-hermiticity. We prove that a kinetic term with continuum and periodic function that is PT symmetric does not reduce doublers. As a simple example, we analyze the two-dimensional two-flavor Gross-Neveu model with minimal doubling fermions. The minimal doubling fermions break PT symmetry and R-hermiticity, hence complex or non-Hermite coupling constants are caused by quantum correction.