HTL quasiparticle picture of the thermodynamics of QCD

Starting from a nonperturbative expression for entropy and density obtained from $\Phi$-derivable two-loop approximations to the thermodynamic potential, a quasiparticle model for the thermodynamics of QCD can be developed which incorporates the physics of hard thermal loops and leads to a reorganization of the otherwise ill-behaved thermal perturbation theory through order $\alpha_s^{3/2}$. Some details of this reorganization are discussed and the differences to simpler quasiparticle models highlighted. A comparison with available lattice data shows remarkable agreement down to temperatures of $\sim 2.5 T_c$.Comment: Talk given at the International Conference on Statistical QCD, Bielefeld, Germany, August 26--30, 2001. 10 pages LATEX, 7 figure

Frozen ghosts in thermal gauge field theory

We review an alternative formulation of gauge field theories at finite temperature where unphysical degrees of freedom of gauge fields and the Faddeev-Popov ghosts are kept at zero temperature.Comment: 6 page

No saturation of the quantum Bogomolnyi bound by two-dimensional supersymmetric solitons

We reanalyse the question whether the quantum Bogomolnyi bound is saturated in the two-dimensional supersymmetric kink and sine-Gordon models. Our starting point is the usual expression for the one-loop correction to the mass of a soliton in terms of sums over zero-point energies. To regulate these sums, most authors put the system in a box with suitable boundary conditions, and impose an ultraviolet cut-off. We distinguish between an energy cut-off and a mode number cut-off, and show that they lead to different results. We claim that only the mode cut-off yields correct results, and only if one considers exactly the same number of bosonic and fermionic modes in the total sum over bound-state and zero-point energies. To substantiate this claim, we show that in the sine-Gordon model only the mode cut-off yields a result for the quantum soliton mass that is consistent with the exact result for the spectrum as obtained by Dashen et al. from quantising the so-called breather solution. In the supersymmetric case, our conclusion is that contrary to previous claims the quantum Bogomolnyi bound is not saturated in any of the two-dimensional models considered.Comment: 23 pages, LATe

On the imaginary part of the next-to-leading-order static gluon self-energy in an anisotropic plasma

Using hard-loop (HL) effective theory for an anisotropic non-Abelian plasma, which even in the static limit involves nonvanishing HL vertices, we calculate the imaginary part of the static next-to-leading-order gluon self energy in the limit of a small anisotropy and with external momentum parallel to the anisotropy direction. At leading order, the static propagator has space-like poles corresponding to plasma instabilities. On the basis of a calculation using bare vertices, it has been conjectured that, at next-to-leading order, the static gluon self energy acquires an imaginary part which regulates these space-like poles. We find that the one-loop resummed expression taken over naively from the imaginary-time formalism does yield a nonvanishing imaginary part even after including all HL vertices. However, this result is not correct. Starting from the real-time formalism, which is required in a non-equilibrium situation, we construct a resummed retarded HL propagator with correct causality properties and show that the static limit of the retarded one-loop-resummed gluon self-energy is real. This result is also required for the time-ordered propagator to exist at next-to-leading order.Comment: REVTEX, 15 pages, 4 figures. v2: slightly shortened title, shorter appendix

Thermal Green's Functions from Quantum Mechanical Path Integrals

In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum mechanical path integral. With this calculational approach one avoids the loop-momentum integrals usually encountered in Feynman perturbation theory, although with thermal Green's functions, a discrete sum (over the winding numbers of paths with respect to the circular imaginary time) must be computed. The high-temperature expansion of this sum can be performed for all Green's functions at the same time, and is particularly simple for the static case. The procedure is illustrated by evaluating the two-point function to one-loop order in a $\phi^3_6$ model.Comment: 13 p., uses REVTEX (updated to REVTEX v3.0; minor corrections and extensions) TUW-92-1