Perturbative QCD at finite temperature and density

This is a comprehensive review on the perturbative hot QCD including the recent developments. The main body of the review is concentrated upon dealing with physical quantities like reaction rates. Contents: \S1. Introduction, \S2. Perturbative thermal field theory: Feynman rules, \S3. Reaction-rate formula, \S4. Hard-thermal-loop resummation scheme in hot QCD, \S5. Effective action, \S6. Hard modes with $|P^2| \leq O (g^2 T^2)$, \S7. Application to the computation of physical quantities, \S8. Beyond the hard-thermal-loop resummation scheme, \S9. Conclusions.Comment: 21page

Renormalization of number density in nonequilibrium quantum-field theory and absence of pinch singularities

Through introducing a notion of renormalization of particle-number density, a simple perturbation scheme of nonequilibrium quantum-field theory is proposed. In terms of the renormalized particle-distribution functions, which characterize the system, the structure of the scheme (and then also the structure of amplitudes and reaction rates) are the same as in the equilibrium thermal field theory. Then, as an obvious consequence, the amplitudes and reaction rates computed in this scheme are free from pinch singularities due to multiple products of $\delta$-functions, which inevitably present in traditional perturbation scheme.Comment: 12page

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

Gauge-boson propagator in out of equilibrium quantum-field system and the Boltzmann equation

We construct from first principles a perturbative framework for studying nonequilibrium quantum-field systems that include gauge bosons. The system of our concern is quasiuniform system near equilibrium or nonequilibrium quasistationary system. We employ the closed-time-path formalism and use the so-called gradient approximation. No further approximation is introduced. We construct a gauge-boson propagator, with which a well-defined perturbative framework is formulated. In the course of construction of the framework, we obtain the generalized Boltzmann equation (GBE) that describes the evolution of the number-density functions of gauge-bosonic quasiparticles. The framework allows us to compute the reaction rate for any process taking place in the system. Various processes, in turn, cause an evolution of the systems, which is described by the GBE.Comment: 28 page

Comment on " Infrared and pinching singularities in out of equilibrium QCD plasmas''

Analyzing the dilepton production from out of equilibrium quark-gluon plasma, Le Bellac and Mabilat have recently pointed out that, in the reaction rate, the cancellation of mass (collinear) singularities takes place only in physical gauges, and not in covariant gauges. They then have estimated the contribution involving pinching singularities. After giving a general argument for the gauge independence of the production rate, we explicitly confirm the gauge independence of the mass-singular part. The contribution involving pinching singularities develops mass singularities, which is also gauge dependent. This `` additional'' contribution to the singular part is responsible for the gauge independence of the `` total'' singular part. We give a sufficient condition, under which cancellation of mass singularities takes place.Comment: 11page