QCD potentials with dynamical quarks at finite temperatures

We investigate the potential between a static quark-antiquark pair in the full QCD vacuum. The dynamical quark sea is considered both by Kogut-Susskind and Wilson fermions. Two temperatures T below and above the phase transition T_c are studied. The behavior of the interquark potential in the full quantum field is driven by the explicitly broken Z₃ symmetry in the fermionic action for T<T_c and by an additional spontaneous Z₃ symmetry breaking for T<T_c.     

Perturbative QED and QCD at finite temperatures and densities

The finite temperature and density QED and QCD are discussed from the perturbative viewpoint. A comparison between Abelian QED and non-Abelian QCD is made at every step. The calculation of the thermodynamic potential is performed up to ² In, allowing the masses of the fermions to be arbitrary. The equation of state for QCD plasma is obtained and the phase transition to the hadronic phase is discussed.     

QCD at finite temperature

Quantum chromodynamics is studied at finite temperatures and densities using the temperature Green functions method. For the Green functions the renormalized Schwinger-Dyson equations are obtained and their qualitative properties are discussed. The equality of the renormalization constants for the equations obtained at T, μ ≠ 0 with those for quantum field theory is pointed out. General properties of the gluon polarization tensor are investigated at T, μ ≠ 0. The temperature Green functions are calculated within the one-loop approximation using both relativistic and axial gauges. The fulfilment of the Slavnov-Taylor identities is verified. The asymptotic behaviour of the polarization tensor at T, μ ≠ 0 is established and the excitation spectrum of quark-gluon plasma is found. Both Fermi and Bose excitations are considered and the gauge invariance of the spectra is demonstrated. The renormalization group extension of the dispersion laws into the regions of high temperatures and densities is presented. The exact representation of the thermodynamical potential in QCD is found in terms of the temperature Green functions. For the quark-gluon plasma the thermodynamical potential is calculated with the g³-term taken into account. The equation of state of the hot quark-gluon plasma is found and its properties are discussed. The complete evolutional diagram of the hadronic matter is outlined. The phase curve asymptotics, which put bounds on the quark-gluon plasma domain, are found for the two limiting cases (μ = 0, T → T₀; T = 0, μ → μ₀). The phase transition of the hot quark-gluon plasma placed in external Abelian field is studied. The instability of such plasma has been found and the program of its stabilization is indicated. The infrared behaviour of the non-Abelian gauge theory is studied for finite temperatures when power divergencies are essential. The propagator of transverse gluons is shown to be singular for momenta |p| ˜ g²T and this cannot be avoided by summing the simplest bubble chains. The infrared asymptotic behaviour of the tree-gluon vertex is found and the results obtained are checked using the Slavnov-Taylor identities. The Green functions asymptotics found indicate either an instability of the quark-gluon plasma in the infrared momentum domain or the inconsistency of the perturbational methods. A non-perturbative approach to the infrared problem in QCD is developed within the axial gauge. The closed equations for the structure functions that determine the gluon polarization tensor are obtained by using the Slavnov-Taylor identities to found approximately the three-gluon vertex. It is shown that the solution of the equations obtained by iterations does not remove the infrared singularity from the temperature Green functions. The nonperturbative solution of such equations is discussed.     

QCD at finite isospin density

QCD at finite isospin chemical potential mu(I) has no fermion sign problem and can be studied on the lattice. We solve this theory analytically in two limits: at low mu(I), where chiral perturbation theory is applicable, and at asymptotically high mu(I), where perturbative QCD works. At low isospin density the ground state is a pion condensate, whereas at high density it is a Fermi liquid with Cooper pairing. The pairs carry the same quantum numbers as the pion. This leads us to conjecture that the transition from hadron to quark matter is smooth, which passes several tests. Our results imply a nontrivial phase diagram in the space of temperature and chemical potentials of isospin and baryon number.     

Infrared finite S-matrix in the QCD coherent state basis

The infrared (IR) structure of the S-matrix in the basis of the QCD coherent states is studied. To any order perturbation theory it is shown that these matrix elements areIR finite in spite of the fact that they involve any number of soft gluons; moreover, these soft gluons do not even contribute to the IR singular part of the inclusive Bloch-Nordsieck distribution. Finally, the BRS charge related to the coherent state S-matrix elements is given and shown to be IR finite to any order perturbation theory.     

QCD sum rules at finite temperature

Finite energy and Laplace transform QCD sum rules atT0 are analyzed, and predictions for vacuum condensates are compared with the low temperature expansion of the energy density and pressure. Results show a serious disagreement which indicates a breakdown of the FESR programme already at dimension four, and which invalidates Laplace transform sum rules, at least in their straightforward extension to finite temperature.     

Quasi-particles at finite temperatures

We study the consequences of the KMS-condition on the properties of quasi-particles, assuming their existence. We establish

1. If the correlation functions decay sufficiently, we can create them by quasi-free field operators.
2. The outgoing and incoming quasi-free fields coincide, there is no scattering.
3. There are may age-operatorsT conjugate toH. For special forms of the dispersion law ε(k) of the quasi-particles there is aT commuting with the number of quasi-particles and its time-monotonicity describes how the quasi-particles travel to infinity.

     

The effective QCD lagrangian at finite temperature

We evaluate the one-loop effective potential at finite temperature for QCD. High-temperature as well as low-temperature limits are investigated. We do not find a phase transition, i.e., the asymmetric Copenhagen ground state is maintained for any temperature.     

Lattice QCD at finite temperature and density

QCD at finite temperature and density is becoming increasingly important for various experimental programmes, ranging from heavy ion physics to astro-particle physics. The non-perturbative nature of non-abelian quantum field theories at finite temperature leaves lattice QCD as the only tool by which we may hope to come to reliable predictions from first principles. This requires careful extrapolations to the thermodynamic, chiral and continuum limits in order to eliminate systematic effects introduced by the discretization procedure. After an introduction to lattice QCD at finite temperature and density, its possibilities and current systematic limitations, a review of present numerical results is given. In particular, plasma properties such as the equation of state, screening masses, static quark free energies and spectral functions are discussed, as well as the critical temperature and the QCD phase structure at zero and finite density.     

QCD at finite density and color superconductivity

The paper contains a brief review of recent applications of many-body theory to quark matter. We discuss the progress in theory of dense quark matter during the last two years, especially color superconductivity. We emphasize that there are two basic dynamical reasons for it: short-range forces induced by instantons and long-range ones mediated by exchanges of magnetic gluons. For quark matter which is supposed to be found in neutron stars, both lead to superconducting gaps on the order of 100 MeV. The most surprising facts are the rather impressive richness of different phases and their robustness in respect to variation of the fundamental interaction.     

Nonperturbative phenomena in QCD at finite temperature

The main objective of the present study is to analyze various nonperturbative phenomena in QCD both at low, T < T _c , and at high, T > T _c , temperatures. New methods are developed that make it possible, on one hand, to describe data obtained by numerically simulating QCD on a lattice and, on the other hand, to study new physical phenomena in QCD at finite temperature.     

Gross features of finite nuclei at finite temperatures

A simple expression is obtained for the low-temperature behaviour of the energy and entropy of finite nuclei for 20 ￡ leq A ￡ leq 250 . The dependence on A of these quantities is for the most part due to the presence of the asymmetry energy.     

Singularity structure of massless QCD at finite temperature

A complete relativistic calculation to first order in the strong coupling constantα _s is presented for deep inelastic scattering of leptons off a heat bath of quarks and gluons. The singularity structure is studied and the cancellation of all collinear and infrared divergences is proven. It is shown that it is necessary to include all processes of a given order (i.e. not only the gluon emission and absorption as usually stated). We show that for non-equilibriumn _F andn _B distributions the collinear singularities do not cancel.