Finite Density Fat QCD

Lattice formulation of Finite Baryon Density QCD is problematic from computer simulation point of view; it is well known that for light quark masses the reconstructed partition function fails to be positive in a wide region of parameter space. For large bare quark masses, instead, it is possible to obtain more sensible results; problems are still present but restricted to a small region. We present evidence for a saturation transition independent from the gauge coupling $\beta$ and for a transition line that, starting from the temperature critical point at $\mu=0$, moves towards smaller $\beta$ with increasing $\mu$ as expected from simplified phenomenological arguments.Comment: 14 pages, 10 figure

Hadronic property at finite density

We report on three topics on finite density simulations: (i) the derivative method for hadronic quantities, (ii) phase fluctuations in the vicinity of the critical temperature and (iii) the density of states method at finite isospin density.Comment: 11 pages, 11 figures, talk given at Finite Density QCD, at Nara, Japan 10-12 July 200

Frustration in Finite Density QCD

We present a detailed analysis of the QCD partition function in the Grand Canonical formalism. Using the fugacity expansion we find evidence for numerical instabilities in the standard evaluation of its coefficients. We discuss the origin of this problem and propose an issue to it. The correct analysis shows no evidence for a discontinuity in the baryonic density in the strong coupling limit. The moderate optimism that was inspired by the Grand Canonical Partition Function calculations in the last years has to be considered ill-founded.Comment: 9 pages, 6 Postscript figures; some comments adde

Pion properties at finite density

In this talk, we report our recent work on the pion weak decay constant (F_pi) and pion mass (m_pi) using the nonlocal chiral quark model with the finite quark-number chemical potential (mu) taken into account. Considering the breakdown of Lorentz invariance at finite density, the time and space components are computed separately, and the corresponding results turn out to be: F^t_pi = 82.96 MeV and F^s_pi = 80.29 MeV at mu_c ~ 320 MeV, respectively. Using the in-medium Gell-Mann Oakes-Renner (GOR) relation, we show that the pion mass increases by about 15% at mu_c.Comment: 5 pages, 2 figures, Talk given at the 4th Asia-Pacific Conference on Few-Body Problems in Physics 2008 (APFB08), 19 ~ 23 Aug 2008, Depok, Indonesi

Field Redefinitions at Finite Density

The apparent dependence of nuclear matter observables on off-shell properties of the two-nucleon potential is re-examined in the context of the effective field theory (EFT) approach. Finite density (thermodynamic) observables are invariant under field redefinitions, which extends the well-known theorem about the invariance of S-matrix elements. Simple examples demonstrate how field redefinitions can shift contributions between purely off-shell two-body interactions and many-body forces, leaving both scattering and finite-density observables unchanged. If only the transformed two-body potentials are kept, however, the nuclear matter binding curves will depend on the off-shell part (generating ``Coester bands''). The correspondence between field redefinitions and unitary transformations, which have traditionally been used to generate ``phase-equivalent'' nucleon-nucleon potentials, is also demonstrated.Comment: 23 pages, RevTex, 9 ps figures, included with epsf.tex, minor change

Lattice QCD at Finite Density

I discuss different approaches to finite density lattice QCD. In particular, I focus on the structure of the phase diagram and discuss attempts to determine the location of the critical end-point. Recent results on the transiton line as function of the chemical potential ($T_c(\mu_q)$) are reviewed. Along the transition line, hadronic fluctuations have been calculated, which can be used to characterize properties of the Quark Gluon plasma and eventually can also help to identify the location of the critical end-point in the QCD phase diagram on the lattice and in heavy ion experiments. Furthermore, I comment on the structure of the phase diagram at large $\mu_q$.Comment: Plenary talk at XXIVth International Symposium on Lattice Field Theory (Lattice 2006). Version to appear as PoS (LAT2006) 021; references adde

Lattice QCD at finite density

QCD at finite density presents specific challenges to lattice gauge theory. Nonetheless, a region of the QCD phase diagram up to moderately large baryon chemical potentials has been successfully explored on the lattice and new results and idea are continuously emerging. I will outline the lattice formulation of QCD, introduce the calculational schemes currently used to treat a nonzero baryon density, and mention lattice methods alternative to MonteCarlo, including the strong coupling expansion which might give access to the the superconducting phase of QCD. The results for the critical line, and the different phases will be discussed highlighting the strength of the different methods, as well as the possible comparisons with phenomenological models.Comment: 14 pages; to appear in the proceedings of Workshop on Finite Density QCD at Nara, Nara, Japan, 10-12 July 200

Results on Finite Density QCD

A brief summary of the formulation of QCD at finite chemical potental, $\mu$, is presented. The failure of the quenched approximation to the problem is reviewed. Results are presented for dynamical simulations of the theory at strong and intermediate couplings. We find that the problems associated with the quenched theory persist: the onset of non-zero quark number does seem to occur at a chemical potential $\approx { {m_{\pi}} \over 2}$. However analysis of the Lee-Yang zeros of the grand canonical partition function in the complex fugacity plane, ($e^{\mu/T}$), does show signals of critical behaviour in the expected region of chemical potential. Results are presented for a simulation at finite density of the Gross-Neveu model on a $16^3$ lattice near to the chiral limit. Contrary to our simulations of QCD no pathologies were found when $\mu$ passed through the value m_{\pi}/2}.Comment: 14 pages, Latex, 18 eps figures, Review for Tsukuba worksho

Chiral Lagrangians at finite density

The effective SU(2) chiral Lagrangian with external sources is given in the presence of non-vanishing nucleon densities by calculating the in-medium contributions of the chiral pion-nucleon Lagrangian. As a by product, a relativistic quantum field theory for Fermi many-particle systems at zero temperature is directly derived from relativistic quantum field theory with functional methods.Comment: 6 Pages, 3 figures, REVTeX. Extended version. Explicit Feynman rules are give