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
In the present work we are interested in understanding various properties of quark matter subject... more In the present work we are interested in understanding various properties of quark matter subject to strong magnetic fields described by the Nambu-Jona-Lasinio model with Polyakov loop. We start by analysing the differences arising from two different vector interactions in the Lagrangian densities, at zero temperature, and apply the results to stellar matter. We then investigate the position of the critical end point for different chemical potential and density scenarios.
The method of optimized perturbation theory (OPT) is used to study the phase diagram of the massl... more The method of optimized perturbation theory (OPT) is used to study the phase diagram of the massless Gross-Neveu model in 2 + 1 dimensions. In the temperature and chemical potential plane, our results give strong support to the existence of a tricritical point and line of first order phase transition, previously only suspected to exist from extensive lattice Monte Carlo simulations. In addition of presenting these results we discuss how the OPT can be implemented in conjunction with the Landau expansion in order to determine all the relevant critical quantities.
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.
Two-loop corrections for the standard Abelian Nambu-Jona-Lasinio model are obtained with the Opti... more Two-loop corrections for the standard Abelian Nambu-Jona-Lasinio model are obtained with the Optimized Perturbation Theory (OPT) method. These contributions improve the usual mean-field and Hartree-Fock results by generating a 1/Nc suppressed term, which only contributes at finite chemical potential. We take the zero temperature limit observing that, within the OPT, chiral symmetry is restored at a higher chemical potential µ, while the resulting equation of state is stiffer than the one obtained when mean-field is applied to the standard version of the model. In order to understand the physical nature of these finite Nc contributions, we perform a numerical analysis to show that the OPT quantum corrections mimic effective repulsive vector-vector interaction contributions. We also derive a simple analytical approximation for the mass gap, accurate at the percent level, matching the mean-field approximation extended by an extra vector channel to OPT. For µ µc the effective vector coupling matching OPT is numerically close (for the Abelian model) to the Fierz-induced Hartree-Fock value G/(2Nc), where G is the scalar coupling, and then increases with µ in a well-determined manner.
The purpose of this work is to show explicitly, that the use of an exponential cut-off regulariza... more The purpose of this work is to show explicitly, that the use of an exponential cut-off regularization scheme in the calculation of Casimir energy densities in S N may lead to conflicting results when compared to those found with the aid of zeta function methods. The main issue is that the latter scheme always delivers finite results, while the former produces some extra divergent terms which are not of easy interpretation
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.
We investigate the convergence properties of optimized perturbation theory, or linear δ expansion... more We investigate the convergence properties of optimized perturbation theory, or linear δ expansion (LDE), within the context of finite temperature phase transitions. Our results prove the reliability of these methods, recently employed in the determination of the critical temperature Tc for a system of weakly interacting homogeneous dilute Bose gas. We carry out the explicit LDE optimized calculations and also the infrared analysis of the relevant quantities involved in the determination of Tc in the large-N limit, when the relevant effective static action describing the system is extended to O(N ) symmetry. Then, using an efficient resummation method, we show how the LDE can exactly reproduce the known large-N result for Tc already at the first non-trivial order. Next, we consider the finite N = 2 case where, using similar resummation techniques, we improve the analytical results for the nonperturbative terms involved in the expression for the critical temperature allowing comparison with recent Monte Carlo estimates of them. To illustrate the method we have considered a simple geometric series showing how the procedure as a whole works consistently in a general case.
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.
Using optimized perturbation theory, we evaluate the effective potential for the massless two dim... more Using optimized perturbation theory, we evaluate the effective potential for the massless two dimensional Gross-Neveu model at finite temperature and density containing corrections beyond the leading large-N contribution. For large-N , our results exactly reproduce the well known 1/N leading order results for the critical temperature, chemical potential and tricritical points. For finite N , our critical values are smaller than the ones predicted by the large-N approximation and seem to observe Landau's theorem for phase transitions in one space dimension. New analytical results are presented for the tricritical points that include 1/N corrections. The easiness with which the calculations and renormalization are carried out allied to the seemingly convergent optimized results displayed, in this particular application, show the robustness of this method and allows us to obtain neat analytical expressions for the critical as well as tricritical values beyond the results currently known.
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
In the present work we are interested in understanding various properties of quark matter subject... more In the present work we are interested in understanding various properties of quark matter subject to strong magnetic fields described by the Nambu-Jona-Lasinio model with Polyakov loop. We start by analysing the differences arising from two different vector interactions in the Lagrangian densities, at zero temperature, and apply the results to stellar matter. We then investigate the position of the critical end point for different chemical potential and density scenarios.
The method of optimized perturbation theory (OPT) is used to study the phase diagram of the massl... more The method of optimized perturbation theory (OPT) is used to study the phase diagram of the massless Gross-Neveu model in 2 + 1 dimensions. In the temperature and chemical potential plane, our results give strong support to the existence of a tricritical point and line of first order phase transition, previously only suspected to exist from extensive lattice Monte Carlo simulations. In addition of presenting these results we discuss how the OPT can be implemented in conjunction with the Landau expansion in order to determine all the relevant critical quantities.
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.
Two-loop corrections for the standard Abelian Nambu-Jona-Lasinio model are obtained with the Opti... more Two-loop corrections for the standard Abelian Nambu-Jona-Lasinio model are obtained with the Optimized Perturbation Theory (OPT) method. These contributions improve the usual mean-field and Hartree-Fock results by generating a 1/Nc suppressed term, which only contributes at finite chemical potential. We take the zero temperature limit observing that, within the OPT, chiral symmetry is restored at a higher chemical potential µ, while the resulting equation of state is stiffer than the one obtained when mean-field is applied to the standard version of the model. In order to understand the physical nature of these finite Nc contributions, we perform a numerical analysis to show that the OPT quantum corrections mimic effective repulsive vector-vector interaction contributions. We also derive a simple analytical approximation for the mass gap, accurate at the percent level, matching the mean-field approximation extended by an extra vector channel to OPT. For µ µc the effective vector coupling matching OPT is numerically close (for the Abelian model) to the Fierz-induced Hartree-Fock value G/(2Nc), where G is the scalar coupling, and then increases with µ in a well-determined manner.
The purpose of this work is to show explicitly, that the use of an exponential cut-off regulariza... more The purpose of this work is to show explicitly, that the use of an exponential cut-off regularization scheme in the calculation of Casimir energy densities in S N may lead to conflicting results when compared to those found with the aid of zeta function methods. The main issue is that the latter scheme always delivers finite results, while the former produces some extra divergent terms which are not of easy interpretation
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.
We investigate the convergence properties of optimized perturbation theory, or linear δ expansion... more We investigate the convergence properties of optimized perturbation theory, or linear δ expansion (LDE), within the context of finite temperature phase transitions. Our results prove the reliability of these methods, recently employed in the determination of the critical temperature Tc for a system of weakly interacting homogeneous dilute Bose gas. We carry out the explicit LDE optimized calculations and also the infrared analysis of the relevant quantities involved in the determination of Tc in the large-N limit, when the relevant effective static action describing the system is extended to O(N ) symmetry. Then, using an efficient resummation method, we show how the LDE can exactly reproduce the known large-N result for Tc already at the first non-trivial order. Next, we consider the finite N = 2 case where, using similar resummation techniques, we improve the analytical results for the nonperturbative terms involved in the expression for the critical temperature allowing comparison with recent Monte Carlo estimates of them. To illustrate the method we have considered a simple geometric series showing how the procedure as a whole works consistently in a general case.
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.
Using optimized perturbation theory, we evaluate the effective potential for the massless two dim... more Using optimized perturbation theory, we evaluate the effective potential for the massless two dimensional Gross-Neveu model at finite temperature and density containing corrections beyond the leading large-N contribution. For large-N , our results exactly reproduce the well known 1/N leading order results for the critical temperature, chemical potential and tricritical points. For finite N , our critical values are smaller than the ones predicted by the large-N approximation and seem to observe Landau's theorem for phase transitions in one space dimension. New analytical results are presented for the tricritical points that include 1/N corrections. The easiness with which the calculations and renormalization are carried out allied to the seemingly convergent optimized results displayed, in this particular application, show the robustness of this method and allows us to obtain neat analytical expressions for the critical as well as tricritical values beyond the results currently known.
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.
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Papers by Marcus Pinto