arXiv subjects
Publications and source records attributed to Jens O. Andersen.
We calculate numerically the phase diagram of the three-flavor Nambu-Jona-Lasinio model at zero and finite temperature as a function of the up, down, and strange quark chemical potentials. We focus on the competition between pseudoscalar condensation and color superconductivity. We find that the two types of phases are separated by first-order transitions.
We consider the Gross-Neveu model with a continuous chiral symmetry in two and three spacetime dimensions at zero and finite temperature. In order to study long-range phase coherence, we construct an effective low-energy Lagrangian for the phase $θ$. This effective Lagrangian is used to show that the fermionic two-particle correlation function at finite temperature decays algebraically in 2+1 dimensions and exponentially in 1+1 dimensions.
We consider a massive relativistic Bose gas with $N$ complex scalars at finite density. At zero temperature, we calculate the pressure, charge density and the speed of sound in the one-loop approximation. In the nonrelativistic limit, we obtain the classic results for the dilute Bose gas. We also discuss finite-temperature effects. In particular, we consider the problem of calculating the critical temperature for Bose-Einstein condensation. Dimensional reduction and effective-field-theory methods are used to perturbatively calculate the effects of the nonstatic Matsubara modes. Calculations of $T_c$ in the effective 3d theory require nonperturbative methods. Using the Monte Carlo simulations of X. Sun [Phys. Rev. {\bf E67}, 066702 (2003)] and the seven-loop variational perturbation theory (VPT) calculations of B. Kastening [Phys. Rev. {\bf A70}, 043621 (2004)], we obtain $T_c$ for N=2 to second order in the interaction.
There has been significant progress in our understanding of finite-temperature field theory over the past decade. In this paper, we review the progress in perturbative thermal field theory focusing on thermodynamic quantities. We first discuss the breakdown of naive perturbation theory at finite temperature and the need for an effective expansion that resums an infinite class of diagrams in the perturbative expansion. This effective expansion which is due to Braaten and Pisarski, can be used to systematically calculate various static and dynamical quantities as a weak-coupling expansion in powers of g. However, it turns that the weak-coupling expansion for thermodynamic quantities are useless unless the coupling constant is very small. We critically discuss various ways of reorganizing the perturbative series for thermal field theories in order to improve its convergence. These include screened perturbation theory (SPT), hard-thermal-loop perturbation theory (HTLPT), the Phi-derivable approach, dimensionally reduced (DR) SPT, and the DR Phi-derivable approach.
In this paper we examine Phi-derivable approximations in QED. General theorems tell us that the gauge dependence of the n-loop Phi-derivable approximation shows up at order g^(2n) where g is the coupling constant. We consider the gauge dependence of the two-loop Phi-derivable approximation to the Debye mass and show that it is of order e^4 as expected. We solve the three-loop Phi-derivable approximation in QED by expanding sum-integrals in powers of e^2 and m/T, where m is the Debye mass which satisfies a variational gap equation. The results for the pressure and the Debye mass are accurate to order e^5.
The thermodynamics of the O(N) linear and nonlinear sigma models in 3+1 dimensions is studied. We calculate the pressure to next-to-leading order in the 1/N expansion and show that at this order, temperature-independent renormalization is only possible at the minimum of the effective potential. The 1/N expansion is found to be a good expansion for N as low as 4, which is the case relevant for low-energy QCD phenomenology. We consider the cases with and without explicit symmetry breaking. We show that previous next-to-leading order calculations of the pressure are either breaking down in the temperatures of interest, or based on unjustifiable high-energy approximations.
The thermodynamics of the O(N) nonlinear sigma model in 1+1 dimensions is studied. We calculate the pressure to next-to-leading order in the 1/N expansion and show that at this order, only the minimum of the effective potential can be rendered finite by temperature-independent renormalization. To obtain a finite effective potential away from the minimum requires an arbitrary choice of prescription, which implies that the temperature dependence is ambiguous. We show that the problem is linked to thermal infrared renormalons.
We calculate the quark contribution to the free energy of a hot quark-gluon plasma to two-loop order using hard-thermal-loop (HTL) perturbation theory. All ultraviolet divergences can be absorbed into renormalizations of the vacuum energy and the HTL quark and gluon mass parameters. The quark and gluon HTL mass parameters are determined self-consistently by a variational prescription. Combining the quark contribution with the two-loop HTL perturbation theory free energy for pure-glue we obtain the total two-loop QCD free energy. Comparisons are made with lattice estimates of the free energy for N_f=2 and with exact numerical results obtained in the large-N_f limit.
The conventional weak-coupling expansion for thermodynamic quantities in hot field theories shows poor convergence unless the coupling constant is tiny. I discuss screened perturbation theory (SPT) which is a way of reorganizing the perturbative expansion for scalar theories %by adding and subtracting a local mass term in the Lagrangian, and hard-thermal-loop perturbation theory (HTLPT), which is its generalization to gauge theories. I present results for the pressure to three loops in SPT and to two loops in HTLPT. We compare the latter with three- and four-dimensional lattice simulations of pure-glue QCD.
We consider nonrelativistic superfluids where the global U(1)-symmetry is spontaneously broken. At sufficiently long wavelengths, the relevant degree of freedom is the massless Goldstone mode and we construct an effective low energy theory for the Goldstone boson. The damping rate of collective excitations at low energy is calculated. In the case of a weakly interacting Bose gas, we recover the results by Beliaev, and by Hohenberg and Martin.
We calculate the equation of state for degenerate quark matter to leading order in hard-dense-loop (HDL) perturbation theory. We solve the Tolman-Oppenheimer-Volkov equations to obtain the mass-radius relation for dense quark stars. Both the perturbative QCD and the HDL equations of state have a large variation with respect to the renormalization scale for quark chemical potential below 1 GeV which leads to large theoretical uncertainties in the quark star mass-radius relation.
We calculate the pressure for pure-glue QCD at high temperature to two-loop order using hard-thermal-loop (HTL) perturbation theory. At this order, all the ultraviolet divergences can be absorbed into renormalizations of the vacuum energy density and the HTL mass parameter. We determine the HTL mass parameter by a variational prescription. The resulting predictions for the pressure fail to agree with results from lattice gauge theory at temperatures for which they are available.
We consider an interacting homogeneous Bose gas at zero temperature in two spatial dimensions. The properties of the system can be calculated as an expansion in powers of g, where g is the coupling constant. We calculate the ground state pressure and the ground state energy density to second order in the quantum loop expansion. The renormalization group is used to sum up leading and subleading logarithms from all orders in perturbation theory. In the dilute limit, the renormalization group improved pressure and energy density are essentially expansions in powers of the T-matrix.
QED is studied at low temperature ($T\ll m$, where $m$ is the electron mass) and zero chemical potential. By integrating out the electron field and the nonzero bosonic Matsubara modes, we construct an effective three-dimensional field theory that is valid at distances $R\gg1/T$. As applications, we reproduce the ring-improved free energy and calculate the Debye mass to order $e^5$.
We discuss corrections to the Casimir effect at finite temperature and effective field theory. Recently, it has been shown that effective field theories can reproduce radiative corrections to the Casimir energy calculated in full QED. We apply effective field theory methods at finite temperature and reproduce the Casimir free energy. We show that the system undergoes dimensional reduction at high temperature and that it can be described by an effective three-dimensional field theory.
The thermal physics of a massless scalar field with a phi^4 interaction is studied within screened perturbation theory (SPT). In this method the perturbative expansion is reorganized by adding and subtracting a mass term in the lagrangian. We consider several different mass prescriptions that generalize the one-loop gap equation to two-loop order. We calculate the pressure and entropy to three-loop order and the screening mass to two-loop order. In contrast to the weak-coupling expansion, the SPT-improved approximations appear to converge even for rather large values of the coupling constant.
We consider the ground state of a trapped Bose-Einstein condensate in two dimensions. In the mean-field approximation, the ground state density profile satisfies the Gross-Pitaevskii equation. We compute the leading quantum corrections to the density profile to second order in an expansion around the Thomas-Fermi limit. By summing the ladder diagrams, we are generalizing Schick's result for the ground state energy of a homogeneouns Bose gas to the case of a trapped Bose gas.
The conventional weak-coupling expansion for the pressure of a hot plasma shows no sign of convergence unless the the coupling constant $g$ is tiny. In this talk, I discuss screened perturbation theory (SPT) which is a reorganization of the perturbative expansion by adding and subtracting a local mass term in the Lagrangian. We consider several different mass prescriptions, and compute the pressure to three-loop order. The SPT-improved approximations appear to converge for rather large values of the coupling constant.