Ferromagnetism in quark matter

We investigate the magnetic property of the cold quark matter employing the magnetic moment $\vec{\mu}'$ as the order parameter. Through analysis of the effective potential $V (\vec{\mu}^{' 2})$, we find that, at relatively high densities $\rho > \rho_c$, the quark matter is in the normal phase. At $\rho = \rho_c$, the magnetic phase transition takes place and, in the low-density region $\rho < \rho_c$, the quark matter is in the ferromagnetic phase. For up, down and strange quarks, $\rho_c = 1.62 \rho_0$, $1.47 \rho_0$ and $2.20 \rho_0$ ($\rho_0$ the nuclear density), respectively. We also find that the leptons ($e$ and $\mu$) inside the quark matter are in the normal phase.Comment: 22 pages, 13 figure

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

Improvement of the hot QCD pressure by the minimal sensitivity criterion

The principles of minimal sensitivity (PMS) criterion is applied to the perturbative free energy density, or pressure, of hot QCD, which include the $\sim g_s^6 \ln g_s$ and part of the $\sim g_s^6$ terms. Applications are made separately to the short- and long-distance parts of the pressure. Comparison with the lattice results, at low temperatures, shows that the resultant `` optimal'' approximants are substantially improved when compared to the $\bar{MS}$ results. In particular, for the realistic case of three quark flavors, the `` optimal'' approximants are comparable with the lattice results.Comment: 14 pages, 9 figures, LaTe

Angular intricacies in hot gauge field theories

It is argued that in hot gauge field theories, "Hard Thermal Loops" leading order calculations call for a definite sequence of angular averages and discontinuity (or Imaginary part prescription) operations, and run otherwise into incorrect results. The ten years old collinear singularity problem of hot $QCD$, provides a striking illustration of that fate.Comment: 14 pages, 1 figur

Two-loop Compton and annihilation processes in thermal QCD

We calculate the Compton and annihilation production of a soft static lepton pair in a quark-gluon plasma in the two-loop approximation. We work in the context of the effective perturbative expansion based on the resummation of hard thermal loops. Double counting is avoided by subtracting appropriate counterterms. It is found that the two-loop diagrams give contributions of the same order as the one-loop diagram. Furthermore, these contributions are necessary to obtain agreement with the naive perturbative expansion in the limit of vanishing thermal masses.Comment: Latex, 24 pages, postscript figures included with the package graphic

Self-energy-part resummed quark and gluon propagators in a spin-polarized quark matter and generalized Boltzmann equations

We construct perturbative frameworks for studying nonequilibrium spin-polarized quark matter. We employ the closed-time-path formalism and use the gradient approximation in the derivative expansion. After constructing self-energy-part resummed quark and gluon propagators, we formulate two kind of mutually equivalent perturbative frameworks: The first one is formulated on the basis of the initial-particle distribution function, and the second one is formulated on the basis of `` physical''-particle distribution function. In the course of construction of the second framework, the generalized Boltzmann equations and their relatives {\em directly} come out, which describe the evolution of the system. The frameworks are relevant to the study of a magnetic character of quark matters, e.g., possible quark stars.Comment: 57 page

On the Light Cone Singularity of the Thermal Effective Expansion

We consider a scalar massless quantum field model, at finite temperature $T$, both renormalizable and asymptotically free. Focussing on the singular structure of the effective perturbation theory about the light cone, several new insights are put forth, regarding the interplay between hard thermal loop resummation and the overall compensation of collinear singularities.Comment: 18 page

Proof of a mass singularity free property in high temperature QCD

It is shown that three series of diagrams entering the calculation of some hot $QCD$ process, are mass (or collinear) singularity free, indeed. This generalizes a result which was recently established up to the third non trivial order of (thermal) Perturbation Theory.Comment: 40 pages, 3 figures. to be published in J. Math. Phys. no. 44, 200