Local quantum statistics in arbitrary curved space-time

A local quantum statistics based on a finite temperature field theory in an arbitrary Riemann space-time is considered. The expressions have been derived for the partition functions, the grand thermodynamic potential and the particle distributions 〈n _k〉 of massive scalar gas and fermion gas in arbitrary space-time. It is shown that the chemical potential depends on the geometry of manifold.     

Phase diagram of the Gross-Neveu model: exact results and condensed matter precursors

Recently the revised phase diagram of the (large N) Gross-Neveu model in 1 + 1 dimensions with discrete chiral symmetry has been determined numerically. It features three phases, a massless and a massive Fermi gas and a kink-antikink crystal. Here we investigate the phase diagram by analytical means, mapping the Dirac-Hartree-Fock equation onto the non-relativistic Schrödinger equation with the (single gap) Lamé potential. It is pointed out that mathematically identical phase diagrams appeared in the condensed matter literature some time ago in the context of the Peierls-Fröhlich model and ferromagnetic superconductors.     

Low energy theorems in a nonlocal chiral quark model at finite temperature

We solve the Dyson equation and the Bethe-Salpeter equation for a nonlocal effective quark interaction kernel which is instantaneous and separable. The momentum-dependent dynamical quark mass, the scalar and pseudoscalar meson masses, the pion decay constant and the quark meson coupling constant are calculated at finite temperature in the Hartree approximation for the quark self energy. We obtain relations between these quantities, which coincide to leading order in the current quark mass (m ₀/Δm) with the basic low energy theorems: the Goldstone theorem, the Gell-Mann-Oakes-Renner relation and the Goldberger-Treimann relation at finite temperature. A formula for the σ?π mass gap is obtained which exhibits an additional contribution from the momentum dependence of the quark mass.     

Pion properties at finite isospin chemical potential with isospin symmetry breaking

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 0 and μI 0 in the phase diagram, and different values for the charged pion mass(or decay constant) and neutral pion mass(or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses.     

Gravitational phase transition of fermionic matter in a general-relativistic framework

The Thomas–Fermi model at finite temperature is extended to describe a system of self-gravitating weakly interacting massive fermions in a general-relativistic framework. The existence and properties of the gravitational phase transition in this model are investigated numerically. It is shown that when a nondegenerate gas of weakly interacting massive fermions is cooled below some critical temperature, a condensed phase emerges, consisting of quasidegenerate fermion stars. For fermion masses of 10 to 25 keV, these fermion stars may very well provide an alternative explanation for the supermassive compact dark objects that are observed at galactic centers. Received: 23 April 1999 / Revised version: 24 June 1999 / Published online: 28 September 1999     

Dynamical symmetry breaking in models with the Yukawa interaction

The models with a massless fermion and a self-interacting massive scalar field with the Yukawa interaction are discussed. The chiral condensate and the fermion mass are calculated analytically through a one-loop approximation in (1 + 1)-dimensions. It is shown that the models have a phase transition as a function of the squared mass of the scalar field.     

Physical particles of the massive Schwinger model

The massive Schwinger model is considered in the infinite momentum frame. By assuming its physical particles consist of two fermion bound states, we compute a spectrum. For fermions with large bare masses, the method is reliable. For low-mass fermions, we find we must include states of higher fermion number to adequately describe excited states of the fundamental boson of the theory. We do this for the scalar state in the limit of small bare fermion mass. This representation of the theory provides a unified treatment of both the weak and strong coupling limits, remaining in the fermion representation throughout. We have checked our numerical results with exact calculations wherever possible, and find good agreement.     

Mass spectrum of diquarks and mesons in the color–flavor locked phase of dense quark matter

The spectrum of meson and diquark excitations of dense quark matter is considered in the framework of the Nambu–Jona-Lasinio model with three types of massless quarks in the presence of a quark number chemical potential μ. We investigate the effective action of meson and diquark fields both at sufficiently large values of μ>μ_c≈  330 MeV, where the color–flavor locked (CFL) phase is realized, and in the chirally broken phase of quark matter (μ<μ_c). In the latter case all nine pseudoscalar mesons are Nambu–Goldstone (NG) bosons, whereas the mass of the scalar meson nonet is twice the dynamical quark mass. In the chirally broken phase the pseudoscalar diquarks are not allowed to exist as stable particles, but the scalar diquarks might be stable only at a rather strong interaction in the diquark channel. In the case of the CFL phase, all NG bosons of the model are realized as scalar and pseudoscalar diquarks. Moreover, it turns out that massive diquark excitations are unstable for this phase. In particular, for the scalar and pseudoscalar octets of diquark resonances a mass value around 230 MeV was found numerically. In contrast, mesons are stable particles in the CFL phase. Their masses lie in the interval 400–500 MeV for not too large values of μ>μ_c. PACS 11.30.Qc; 12.38.-t; 12.39.-x     

The calculation of Dirac sea effects on finite solitons

The effects of polarization of the Dirac sea on finite solitons in a simple theory in which fermions interact with a single scalar field are studied. The mass shift for a given background scalar field is computed numerically and compared to approximations arising from expansions in inverse powers of the effective fermion mass and in powers of derivatives of the background scalar field. The conditions under which such approximations succeed are discussed. When such approximations work one can derive local equations of motion for the soliton fields which include the effects of polarizing the Dirac sea. These new equations are studied and energy minimization is used to explore the effects of the Dirac sea on the structure of the soliton. Calculations for a typical Friedberg-Lee soliton are presented, and it is shown that, while the approximations do not work well for fields employed to model the quark structure of nucleons, they do provide an upper bound for the mass of the soliton. A scalar field typical of those used to model ¹⁶O in quantum hadrodynamics is also studied, and it is shown that, when the effective potential is supplemented by the next term occurring in a derivative expansion, the renormalized shift in the energy of the Dirac sea is well approximated.     

Diquark mass differences from unquenched lattice QCD

We calculate diquark correlation functions in the Landau gauge on the lattice using overlap valence quarks and 2+1-flavor domain wall fermion configurations. Quark masses are extracted from the scalar part of quark propagators in the Landau gauge. The scalar diquark quark mass difference and axial vector scalar diquark mass difference are obtained for diquarks composed of two light quarks and of a strange and a light quark. The light sea quark mass dependence of the results is examined. Two lattice spacings are used to check the discretization effects.The coarse and fine lattices are of sizes 24~3×64 and 32~3×64 with inverse spacings 1/a = 1.75(4) Ge V and 2.33(5) Ge V,respectively.     

On the phase structure of QCD in a finite volume

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.     

The MAST FV/FE scheme for the simulation of two-dimensional thermohaline processes in variable-density saturated porous media

A novel methodology for the simulation of 2D thermohaline double diffusive processes, driven by heterogeneous temperature and concentration fields in variable-density saturated porous media, is presented. The stream function is used to describe the flow field and it is defined in terms of mass flux. The partial differential equations governing system is given by the mass conservation equation of the fluid phase written in terms of the mass-based stream function, as well as by the advection–diffusion transport equations of the contaminant concentration and of the heat. The unknown variables are the stream function, the contaminant concentration and the temperature. The governing equations system is solved using a fractional time step procedure, splitting the convective components from the diffusive ones. In the case of existing scalar potential of the flow field, the convective components are solved using a finite volume marching in space and time (MAST) procedure; this solves a sequence of small systems of ordinary differential equations, one for each computational cell, according to the decreasing value of the scalar potential. In the case of variable-density groundwater transport problem, where a scalar potential of the flow field does not exist, a second MAST procedure has to be applied to solve again the ODEs according to the increasing value of a new function, called approximated potential. The diffusive components are solved using a standard Galerkin finite element method. The numerical scheme is validated using literature tests.     

Real-Time Thermal Field Theory Analyses of 2D Gross-Neveu Model

The discrete symmetry breaking and possible restoration at finite temperature T are analyzed in 20 Gross-Neveu model by the real-time thermal field theory in the fermion bubble approximation. The dynamical fermion mass m is proven to, be scale-independent and this fact indicates the equivalence between the fermion bubble diagram approximation and the meanfield approximation used in the auxiliary scalar field approach. Reproducing of the nonzero critical temperature T_c = 0.567m(O), m(0) is the dynamical fermion mass at T = 0, shows the equivalence between the real-time and the imaginary-time thermal. field theories in this problem. However, in the real-time formalism, more results including absence of scalar bound state, the equation of criticality curve of chemical potential-temperature and the ln(T_c/T) behavior of m² at T ≤ T_c can be easily obtained. The last one indicates the second-order phase transition feature of the symmetry restoration.     

Hadron-quark phase coexistence in a hybrid MIT-Bag model

The phase transition of hadronic to quark matter and the boundaries of the hadron-quark coexistence phase are studied within the two Equation of State (EoS) models. The relativistic effective mean-field approach with constant and density-dependent meson-nucleon couplings is used to describe hadronic matter, and the MIT-Bag model is adopted to describe quark matter. The boundaries of the mixed phase for different Bag constants are obtained solving the Gibbs equations. We notice that the dependence on the Bag parameter of the critical temperatures (at zero chemical potential) can be well reproduced by a fermion ultrarelativistic quark gas model, without contribution from the hadron part. At variance, the critical chemical potentials (at zero temperature) are very sensitive to the EoS of the hadron sector. Hence, the contribution of the hadronic interaction is much more relevant for the determination of the transition to the quark-gluon plasma at finite baryon density and low T . Moreover, in the low-temperature and finite chemical potential region no solutions of the Gibbs conditions are existing for small Bag-constant values, B < (135 MeV)⁴ . Isospin effects in asymmetric matter appear important in the high chemical-potential regions at lower temperatures, of interest for the inner-core properties of neutron stars and for heavy-ion collisions at intermediate energies.     

Effective lagrangian analysis of the chiral phase transition at finite density

Introducing a finite chemical potential μ for the quark number density ψ^°ψ, we study analytically the restoration of Π^° chiral symmetry as μ is varied. In the strong coupling limit, the effective lagrangian for SU(N) gauge theories coupled to fermion fields in d dimensions is derived for all N. In the case of SU(2) we predict a second order chiral symmetry restoration phase transition, whereas for all N?3 the transition is first order. Predictions are given for the critical values of the chemical potential μ.     

Nonlinear σ-model and nucleon structure

The nonlinear σ-model with the Wess-Zumino action describes the nucleon as a soliton and incorporates the non-abelian chiral anomalies. Several studies have shown that the model works well except for the nucleon mass, which comes out consistently too large. We investigate this question beginning with the more general framework of the linear σ-model, which has besides a pseudoscalar meson sector, a fermion or quark sector, a scalar field and an interaction between the fermions via the scalar field. Using a path integral formulation, we express the fermion measure of the model as the product of a Jacobian and an invariant measure. Identifying this Jacobian as exp[iΓ _wz] , we find that the model breaks up into two parts, when in the pseudoscalar meson sector the scalar field is replaced by its vacuum value. The pseudoscalar part of the model becomes the nonlinear σ-model with the Wess-Zumino actionΓ _wz. The other part involves chiral fermions, the scalar field and their interaction. We continue this part back to the Minkowski space to determine its ground state and energy levels. We find that for a scalar field that vanishes at smallr, but rises sharply to its vacuum value at someR, the ground state energy of the interacting quark-scalar-field system can be lower than the ground state energy of the non-interacting quark system. This means the interaction between quarks and the scalar field can lead to a condensed ground state or vacuum and can reduce the overall energy of the system (a phase transition as in superconductivity). It is, therfore, not surprising that the nonlinear σ-model predicts too large a nucleon mass, since it implicitly assumes a normal non-interacting vacuum in the quark sector. Quarks are now quasiparticles that appear as excitations of the condensed vacuum. The nucleon structure that emerges from this investigation agrees fully with the phenomenological nucleon structure found from analysis of high energy elasticpp and \(\bar p\) p scattering at CERN ISR and SPS Collider.     

A scalar-fermion model in the limit of infinitely heavy fermions

As a first step in the non-perturbative study of a chiralU(1)?U(1) Yukawa-model with explicit mirror fermions the limit of infinite bare fermion mass is considered. Non-perturbative information is obtained from 14th order scalar hopping parameter expansion, which is confronted with high statistics numerical data. A remarkable universality of the upper bound for the renormalized quartic coupling is observed. A new kind of first order phase transition surface is localized, which is characterized by a large jump in the average field length.     

The equation of state of quarks and mesons in a renormalization group flow picture

Non-perturbative flow equations within an effective linear sigma model coupled to constituent quarks for two quark flavours are derived and solved. A heat kernel regularization is employed for a renormalization group improved effective potential. We determine the initial values of the coupling constants in the effective potential at zero temperature. Solving the evolution equations with the same initial values at finite temperature in the chiral limit, we find a second-order phase transition at T_c≈150 MeV. Due to the smooth decoupling of massive modes, we can directly link the low-temperature four-dimensional theory to the three-dimensional high-temperature theory. We calculate the equation of state in the chiral limit and for finite pion masses and determine universal critical exponents.     

Lattice cut-off effects and their reduction in studies of QCD thermodynamics at non-zero temperature and chemical potential

We clarify the relation between the improvement of dispersion relations in the fermion sector of lattice regularized QCD and the improvement of bulk thermodynamic observables. We show that in the infinite temperature limit the cut-off dependence in dispersion relations can be eliminated up to (aⁿ) corrections, if the quark propagator is chosen to be rotationally invariant up to this order. In bulk thermodynamic observables this eliminates cut-off effects up to the same order at vanishing as well as non-vanishing chemical potential. We furthermore show that in the infinite temperature, ideal gas limit the dependence of finite cut-off corrections on the chemical potential is given by Bernoulli polynomials which are universal as they do not depend on a particular discretization scheme. We explicitly calculate leading and next-to-leading order cut-off corrections for some staggered and Wilson fermion type actions and compare these with exact evaluations of the free fermion partition functions. This also includes the chirally invariant overlap and domain wall fermion formulations. PACS  11.15.Ha; 11.10.Wx; 12.38.Gc; 12.38.Mh     

A Wilson-Yukawa Model with undoubled chiral fermions in 2D

We consider the fermion mass spectrum in the strong coupling vortex phase (VXS) of a lattice fermion-scalar model with a global U(1)_L × U(1)_R, in two dimensions, in the context of a recently proposed two-cutoff lattice formulation. The fermion doublers are made massive by a strong Wilson-Yukawa coupling, but in contrast with the standard formulation of these type of models, in which the light fermion spectrum was found to be vector-like, we find massless fermions with chiral quantum numbers at finite lattice spacing. When the global symmetry is gauged, this model is expected to give rise to a lattice chiral gauge theory.