The optimized linear δ expansion is applied to the λφ4 theory at high temperature. Using the imag... more The optimized linear δ expansion is applied to the λφ4 theory at high temperature. Using the imaginary time formalism the thermal mass is evaluated perturbatively up to order δ2. A variational procedure associated with the method generates nonperturbative results which are used to obtain the critical temperature for the phase transition. Our results are compared with the ones given by propagator dressing methods.
The optimized perturbation theory (OPT) method is applied to the SU(2) version of the Nambu-Jona-... more The optimized perturbation theory (OPT) method is applied to the SU(2) version of the Nambu-Jona-Lasinio (NJL) model both at zero and at finite temperature and/or density. At the first nontrivial order, the OPT exhibits a class of 1/Nc corrections which produce nonperturbative results that go beyond the standard large-Nc or mean-field approximation. The consistency of the OPT method with the Goldstone theorem at this order is established, and appropriate OPT values of the basic NJL (vacuum) parameters are obtained by matching the pion mass and decay constant consistently. Deviations from standard large-Nc relations induced by OPT at this order are derived, for example, for the Gell-Mann-Oakes-Renner relation. Next, the results for the critical quantities and the phase diagram of the model, as well as a number of other thermodynamical quantities of interest, are obtained with OPT and then contrasted with the corresponding results at large Nc.
ABSTRACT We study the phase diagram of the 3d massless Gross–Neveu model with different numbers o... more ABSTRACT We study the phase diagram of the 3d massless Gross–Neveu model with different numbers of fermionic species, N. Using the Optimized Perturbation Theory technique, the free energy is evaluated at finite temperature and chemical potential. The analytical results allow us to calculate critical quantities for any value of N and, in the present work, we choose de values N = 1,3,4,10. In addition, we determine the evolution of the tricritical points, in the temperature versus chemical potential plane for these different values of N.
We analyze the possible transition patterns exhibited by an effective non-relativistic field mode... more We analyze the possible transition patterns exhibited by an effective non-relativistic field model describing interacting binary homogeneous dilute Bose gases whose overall potential is repulsive. We evaluate the temperature dependence of all couplings and show that at intermediate temperatures the crossed interaction, which is allowed to be attractive, dominates, leading to smooth re-entrant phases. At higher temperatures this interaction suffers
ABSTRACT We study the phase diagram of the 3d massless Gross–Neveu model with different numbers o... more ABSTRACT We study the phase diagram of the 3d massless Gross–Neveu model with different numbers of fermionic species, N. Using the Optimized Perturbation Theory technique, the free energy is evaluated at finite temperature and chemical potential. The analytical results allow us to calculate critical quantities for any value of N and, in the present work, we choose de values N = 1,3,4,10. In addition, we determine the evolution of the tricritical points, in the temperature versus chemical potential plane for these different values of N.
In order to analyze optimization issues related to the non-perturbative optimized perturbation th... more In order to analyze optimization issues related to the non-perturbative optimized perturbation theory method we consider the effective potential as well as the fermionic mass for the 2d Gross-Neveu model. A direct comparison within the large-N approximation shows that the results obtained from the effective potential optimization are more efficient unless one uses the renormalization group to improve the mass.
Relativistic Aspects of Nuclear Physics - Proceedings of the Sixth International Workshop, 2001
ABSTRACT We apply the nonperturbative optimized linear delta expansion method to the O(N) scalar ... more ABSTRACT We apply the nonperturbative optimized linear delta expansion method to the O(N) scalar field model in three-dimensions to determine the transition temperature of a dilute homogeneous Bose gas.
Non-Perturbative QCD - Proceedings of the Sixth Workshop, 2002
The linear delta expansion has been succesful in dealing with scalar theories at high temperature... more The linear delta expansion has been succesful in dealing with scalar theories at high temperatures. Here, we review this analytical non perturbative method and present some of the new results which can motivate further development regarding its application to gauge theories.
The optimized linear δ expansion is applied to the λφ4 theory at high temperature. Using the imag... more The optimized linear δ expansion is applied to the λφ4 theory at high temperature. Using the imaginary time formalism the thermal mass is evaluated perturbatively up to order δ2. A variational procedure associated with the method generates nonperturbative results which are used to obtain the critical temperature for the phase transition. Our results are compared with the ones given by propagator dressing methods.
The optimized perturbation theory (OPT) method is applied to the SU(2) version of the Nambu-Jona-... more The optimized perturbation theory (OPT) method is applied to the SU(2) version of the Nambu-Jona-Lasinio (NJL) model both at zero and at finite temperature and/or density. At the first nontrivial order, the OPT exhibits a class of 1/Nc corrections which produce nonperturbative results that go beyond the standard large-Nc or mean-field approximation. The consistency of the OPT method with the Goldstone theorem at this order is established, and appropriate OPT values of the basic NJL (vacuum) parameters are obtained by matching the pion mass and decay constant consistently. Deviations from standard large-Nc relations induced by OPT at this order are derived, for example, for the Gell-Mann-Oakes-Renner relation. Next, the results for the critical quantities and the phase diagram of the model, as well as a number of other thermodynamical quantities of interest, are obtained with OPT and then contrasted with the corresponding results at large Nc.
ABSTRACT We study the phase diagram of the 3d massless Gross–Neveu model with different numbers o... more ABSTRACT We study the phase diagram of the 3d massless Gross–Neveu model with different numbers of fermionic species, N. Using the Optimized Perturbation Theory technique, the free energy is evaluated at finite temperature and chemical potential. The analytical results allow us to calculate critical quantities for any value of N and, in the present work, we choose de values N = 1,3,4,10. In addition, we determine the evolution of the tricritical points, in the temperature versus chemical potential plane for these different values of N.
We analyze the possible transition patterns exhibited by an effective non-relativistic field mode... more We analyze the possible transition patterns exhibited by an effective non-relativistic field model describing interacting binary homogeneous dilute Bose gases whose overall potential is repulsive. We evaluate the temperature dependence of all couplings and show that at intermediate temperatures the crossed interaction, which is allowed to be attractive, dominates, leading to smooth re-entrant phases. At higher temperatures this interaction suffers
ABSTRACT We study the phase diagram of the 3d massless Gross–Neveu model with different numbers o... more ABSTRACT We study the phase diagram of the 3d massless Gross–Neveu model with different numbers of fermionic species, N. Using the Optimized Perturbation Theory technique, the free energy is evaluated at finite temperature and chemical potential. The analytical results allow us to calculate critical quantities for any value of N and, in the present work, we choose de values N = 1,3,4,10. In addition, we determine the evolution of the tricritical points, in the temperature versus chemical potential plane for these different values of N.
In order to analyze optimization issues related to the non-perturbative optimized perturbation th... more In order to analyze optimization issues related to the non-perturbative optimized perturbation theory method we consider the effective potential as well as the fermionic mass for the 2d Gross-Neveu model. A direct comparison within the large-N approximation shows that the results obtained from the effective potential optimization are more efficient unless one uses the renormalization group to improve the mass.
Relativistic Aspects of Nuclear Physics - Proceedings of the Sixth International Workshop, 2001
ABSTRACT We apply the nonperturbative optimized linear delta expansion method to the O(N) scalar ... more ABSTRACT We apply the nonperturbative optimized linear delta expansion method to the O(N) scalar field model in three-dimensions to determine the transition temperature of a dilute homogeneous Bose gas.
Non-Perturbative QCD - Proceedings of the Sixth Workshop, 2002
The linear delta expansion has been succesful in dealing with scalar theories at high temperature... more The linear delta expansion has been succesful in dealing with scalar theories at high temperatures. Here, we review this analytical non perturbative method and present some of the new results which can motivate further development regarding its application to gauge theories.
Uploads