Eduardo Mendel

Functional equations for path-dependent phase factors in Yang-Mills theories☆

Abstract We introduce a gauge-covariant functional derivative for path-dependent quantities, and use it to analyze the behavior of the phase matrix Φ y , x ( Γ )= P Γ exp[-∫ x y A ( x )·d x ], under variations of the contour Γ. We give a general formula for Φ y + δy , x + δx ( Γ ′) for a varied path in terms of Φ y , x ( Γ ), and analyze a gauge-covariant version of the functional wave equation (or “string equation”) for Φ derived by Nambu and by Gervais and Neveu. We conclude that there is still a serious gap in the attempt to derive the string theory from a Yang-Mills theory.

Finite baryon density in lattice simulations and nuclear matter

Abstract A simple model for the partition function of an interacting nucleon gas can explain the early onset of the baryon density observed when using staggered fermions on the lattice at finite chemical potential. The onset, which is very sensitive to the number of lightest nucleon states formed, represents the point where condensation into nuclear matter occurs. The lattice simulations have been done with staggered fermions or 4 degenerate valence quarks, which can bind into 40 lightest nucleons for which the model can fit the early onset as found on the lattice for various quark masses. The statistical model contains scalar interactions, producing attractive energies scaling as ifmN−2, among nucleons which propagate in effective volumes that exclude the hard nucleon cores determined by mω. Extrapolating the number of flavours and masses to the values in nature, where we have 4 lowest nucleon states, the model shows an onset close to the nucleon mass as desired.

Nonperturbative real time propagation at finite temperature

Abstract A new formalism will be presented in order to study real time evolution of quantum systems at finite temperature. Probability distributions for time-correlated observables will be studied non-perturbatively and fully quantized. This works for various systems, including ones with tunneling phenomena. We have obtained good results with some computational methods which can be used on models with several degrees of freedom. Thus it looks feasible to study vacuum tunneling in real time for relevant field theories at finite T.

Nucleon degeneracy on the lattice explains early Baryon density onset

Abstract A simple model for the partition function of an interacting nucleon gas can explain the early onset of the Baryon density observed in lattice calculations at finite chemical potential. The onset which is very sensitive to the number of lightest nucleon states formed represents the point where condensation into nuclear matter occurs. In nature where we have 4 lowest nucleon states the model rightly shows an onset close to the nucleon mass. In contrast, the lattice simulations have been done with staggered fermions (4 degenerate valence quarks), thus binding into 40 lightest nucleons for which the model predicts the early onset as found on the lattice for various quark masses. The statistical model contains Yukawa interactions among nucleons in effective volumes that exclude the hard nucleon cores.

QCD at finite chemical potential

The Bayron density in terms of the Chemical Potential μ is calculated on a large 164 lattice aiming at weaker couplings with finer spacings. The fermionic determinant is also included in a new approximate scheme. The onset of the thermodynamic quantities with μ seems to be still lower than at the nucleon mass.

Hadronic structure by introducing chemical potential

Abstract Hadronic structure can be obtained dynamically by calculating baryon density correlation functions at finite chemical potential μ. Even though preliminary results show some structure, it is not yet clearly identifiable with nucleons due to the early onset with μ of thermodynamic quantities. Analyzing the free Fermi gas suggests to take a much finer lattice to improve these results.

Real time correlations at finite temperature for the ising model.

After having developed a method that measures real time evolution of quantum systems at a finite temperature, we present here the simplest field theory where this scheme can be applied to, namely the 1 + 1 Ising model. We will compute the probability that if a given spin is up, some other spin will be up after a time t, the whole system being at temperature T. We can thus study spatial correlations and relaxation times at finite T. The fixed points that enable the continuum real time limit can be easily found for this model. The ultimate aim is to get to understand real time evolution in more complicated field theories, with quantum effects such as tunneling at finite temperature.

QCD at finite baryon density with t-asymmetric fermions

Susskinds continuous-time fermions, with two flavours, can be latticized using a one-sided time derivative. We are presently investigating the interacting case, where we hope to find the onset at finite

Finite density results for Wilson fermions using the volume method

\mu

Time evolution for quantum systems at finite temperature

at the right place due to the reduced number of flavours. As for these fermions there is only a discrete chiral symmetry left over, the lightness of pions in the broken phase has to be investigated.Susskinds continuous-time fermions, with two flavours, can be latticized using a one-sided time derivative. We are presently investigating the interacting case, where we hope to find the onset at finite μ at the right place due to the reduced number of flavours. As for these fermions there is only a discrete chiral symmetry left over, the lightness of pious in the broken phase has to be investigated.