Quantum Field Theories in Nonextensive Tsallis Statistics

Within the framework of Tsallis statistics with q ~ 1, we construct a perturbation theory for treating relativistic quantum field systems. We find that there appear initial correlations, which do not exist in the Boltzmann-Gibbs statistics. Applying this framework to a quark-gluon plasma, we find that the so-called thermal masses of quarks and gluons are smaller than in the case of Boltzmann-Gibbs statistics.Comment: 16 pages, no figure

Ferromagnetism of two-flavor quark matter in chiral and/or color-superconducting phases at zero and finite temperatures

We study the phase structure of the unpolarized and polarized two-flavor quark matters at zero and finite temperatures within the Nambu--Jona-Lasinio (NJL) model. We focus on the region, which includes the coexisting phase of quark-antiquark and diquark condensates. Generalizing the NJL model so as to describe the polarized quark matter, we compute the thermodynamic potential as a function of the quark chemical potential ($\mu$), the temperature ($T$), and the polarization parameter. The result heavily depends on the ratio $G_D / G_S$, where $G_S$ is the quark-antiquark coupling constant and $G_D$ is the diquark coupling constant. We find that, for small $G_D / G_S$, the "ferromagnetic" phase is energetically favored over the "paramagnetic" phase. On the other hand, for large $G_D / G_S$, there appears the window in the ($\mu, T$)-plane, in which the "paramagnetic" phase is favored.Comment: 25 pages, 10 figure

Nonet meson properties in Nambu--Jona-Lasinio model with dimensional versus cutoff regularization

Nambu--Jona-Lasinio (NJL) model with Kobayashi-Maskawa-'t Hooft (KMT) term is one of low energy effective theory of QCD which includes the $U_A(1)$ anomaly. We investigate nonet meson properties in this model with three flavors of quarks. We employ two type of regularizations the dimensional and sharp cutoff ones. The model parameters are fixed phenomenologically for each regularization. Evaluating the kaon decay constant, the $\eta$ meson mass and the topological susceptibility, we show the regularization dependence of the results and discuss the applicability of the NJL model.Comment: 11 pages, 9 figure

Cancellation of energy-divergences and renormalizability in Coulomb gauge QCD within the Lagrangian formalism

In Coulomb gauge QCD in the Lagrangian formalism, energy divergences arise in individual diagrams. We give a proof on cancellation of these divergences to all orders of perturbation theory without obstructing the algebraic renormalizability of the theory.Comment: 13 pages, 7 figure