Abstract:
Quantum chromodynamics (QCD) at sufficiently high density is expected to undergo a chiral phase transition. Understanding such a transition is of particular importance for neutron star or quark star physics. In Lagrangian SU(3) lattice gauge theory, the standard approach breaks down at large chemical potential $\mu$, due to the complex action problem. The Hamiltonian formulation of lattice QCD doesn't encounter such a problem. In a previous work, we developed a Hamiltonian approach at finite chemical potential $\mu$ and obtained reasonable results in the strong coupling regime. In this paper, we extend the previous work to Wilson fermions. We study the chiral behavior and calculate the vacuum energy, chiral condensate and quark number density, as well as the masses of light hadrons. There is a first order chiral phase transition at zero temperature.

Abstract:
We study the critical behavior of lattice Quantum Chromodynamics (QCD) in the strong coupling approximation with Kogut-Susskind and Wilson fermions at finite temperature ($T$) and zero chemical potential. Using the Hamiltonian formulation we construct a mean field solution to the equation of motion at finite $T$ and use it to study the elementary thermal excitations and to extract some critical exponents characterizing the observed second order phase transition. We find similar critical behaviors for Kogut-Susskind and Wilson fermions at finite $T$

Abstract:
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.

Abstract:
The separation of a heavy quark and antiquark pair leads to the formation of a tube of flux, or "string", which should break in the presence of light quark-antiquark pairs. This expected zero-temperature phenomenon has proven elusive in simulations of lattice QCD. We study mixing between the string state and the two-meson decay channel in QCD with two flavors of dynamical sea quarks. We confirm that mixing is weak and find that it decreases at level crossing. While our study does not show direct effects of internal quark loops, our results, combined with unitarity, give clear confirmation of string breaking.

Abstract:
There has been a great deal of interest in understanding the properties of quantum chromodynamics (QCD) for a finite value of the chemical potential and for finite temperature. Studies have been made of the restoration of chiral symmetry in matter and at finite temperature. The phenomenon of deconfinement is also of great interest, with studies of the temperature dependence of the confining interaction reported recently. In the present work we study the change of the properties of light mesons as the temperature is increased. For this study we make use of a Nambu--Jona-Lasinio (NJL) model that has been generalized to include a covariant model of confinement. The parameters of the confining interaction are made temperature-dependent to take into account what has been learned in lattice simulations of QCD at finite temperature. The constituent quark masses are calculated at finite temperature using the NJL model. A novel feature of our work is the introduction of a temperature dependence of the NJL interaction parameters. (This is a purely phenomenological feature of our model, which we do not attempt to derive from more fundamental considerations.) With the three temperature-dependent aspects of the model mentioned above, we find that the mesons we study are no longer bound when the temperature reaches the critical temperature, $T_c$, which we take to be 170 MeV. We believe that ours is the first model that is able to describe the interplay of chiral symmetry restoration and deconfinement for mesons at finite temperature. The introduction of temperature-dependent coupling constants is a feature of our work whose further consequences should be explored in future work.

Abstract:
I review recent progress in lattice QCD at finite temperature. Results on the transition temperature will be summarized. Recent progress in understanding in-medium modifications of interquark forces and quarkonia spectral functions at finite temperatures is discussed.

Abstract:
I discuss recent developments in finite temperature lattice QCD, including the calculation of the transition temperature, equation of state, color screening and meson spectral functions.

Abstract:
These lectures (given at TASI 2000) provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. Lecture 1 (Ch. 2) is a very vanilla introduction to lattice QCD. Lecture 2 (Ch. 3) describes examples of recent lattice calculations relevant to fixing the parameters of the CKM matrix.

Abstract:
A general introduction into the subject aimed at a general theoretical physics audience. We introduce the sign problem posed by finite density lattice QCD, and we discuss the main methods proposed to circumvent it, with emphasis on the imaginary chemical potential approach. The interrelation between the Taylor expansion and the analytic continuation from imaginary chemical potential is discussed in detail. The main applications to the calculation of the critical line, and to the thermodynamics of the hot and the hadronic phase are reviewed.