Narrow Results

In this paper, we review the calculations that are needed to obtain the bosonic and fermionic effective potential at finite temperature and volume (at one loop). The calculations at finite volume correspond to S¹ × R^d topology. These calculations appear in the calculation of the Casimir energy and of the effective potential of extra dimensional theories. In the case of finite volume corrections, we impose twisted boundary conditions and obtain semi-analytic results. We mainly focus in the details and validity of the results. The zeta function regularization method is used to regularize the infinite summations. Also the dimensional regularization method is used in order to renormalize the UV singularities of the integrations over momentum space. The approximations and expansions are carried out within the perturbative limits. After the end of each section, we briefly present applications associated to the calculations. Particularly the calculation of the effective potential at finite temperature for the standard model fields, the effective potential for warped and large extra dimensions, and the topological mass creation. In the end, we discuss on the convergence and validity of one of the obtained semi-analytic results.

We discuss thermodynamic stability of neutral real (quantum) matter from the point of view of a computer experiment at finite, nonzero, temperature. We perform (restricted) path integral Monte Carlo simulations of the two component plasma where the two species are both bosons, both fermions, and one boson and one fermion. We calculate the structure of the plasma and discuss about the formation of binded couples of oppositely charged particles. The purely bosonic case is thermodynamically unstable. In this case we find an undetermined size-dependent contact value unlike partial radial distribution function. For the purely fermionic case, we find a demixing transition with binding also of like species.

We study through a computer experiment, using the restricted path integral Monte Carlo method, a one-component fermion plasma on a sphere at finite, nonzero, temperature. We extract thermodynamic properties like the kinetic and internal energy per particle and structural properties like the radial distribution function. This study could be relevant for the characterization and better understanding of the electronic properties of hollow graphene spheres.

We report on results about the mass sensitivity of chiral symmetry restoration in the linear sigma model. For masses of the pseudoscalar meson octet which are close to the experimental values, we observed only a gradual change in the order parameters, when the temperature was changed. To estimate the size of the first order transition region around the chiral limit, we have varied the mass input for the tree level parametrization in several ways. The point with realistic meson masses turned out to lie well inside the crossover region.

We investigate vacuum transitions in lattice higgs models at finite temperature. The 2 dimensional U(1) Higgs model is used as a toy model. In the 4 dimensional SU(2) Higgs model the region of the phase transition and temperatures above it are considered. The couplings (β, κ, λ) = (2.25, 0.27, 0.5) and (8.0, 0.12996, 0.0017235) correspond to masses in lattice units (a_σm_H, a_σm_w) of (0.02, 0.05) and (0.2,0.2), respectively. The algorithm is described and a parallelized version is proposed. Taking the influence of the finite lattice into account we discuss temperature effects. We compare our results with perturbative estimates and claim that they link low and high temperature approximations.

The dynamical breaking of the supergauge symmetry in the massless supergauge Wess–Zumino model is discussed without adding the Fayet–Iliopoulos term to the Lagrangian. It is shown, in terms of the Nambu–Jona-Lasinio mechanism, that the supergauge symmetry breaking can be realized dynamically in the massless supergauge Wess–Zumino model. The supergauge symmetry behavior at finite temperatures is also investigated and it is shown that the supergauge symmetry broken dynamically at zero temperature can be restored at finite temperatures.

The infrared behavior of Yang–Mills theory at finite temperature provides access to the role of confinement. In this review recent results on this topic from lattice calculations and especially Dyson–Schwinger studies are discussed. These indicate persistence of a residual confinement even in the high-temperature phase. The confinement mechanism is very similar to the one in the vacuum for the chromomagnetic sector. In the chromoelectric sector screening occurs at the soft scale g²T, although not leading to a perturbative behavior.

We have introduced the Cornwall–Jackiw–Tomboulis (CJT) resummation scheme in studying nuclear matter. Based on the CJT formalism and using Walecka model, we have derived a set of coupled Dyson equations of nucleons and mesons. Neglecting the medium effects of the mesons, the usual mean field theory (MFT) results can be obtained. The beyond MFT calculations have been performed by thermodynamic consistently determining the meson effective masses and solving the coupled gap equations for nucleons and mesons together. The numerical results for the nucleon and meson effective masses at finite temperature and chemical potential in nuclear matter are discussed.

The in-medium properties of charm mesons (D and ) in a hot and dense matter are studied. A self-consistent coupled-channel approach is driven by a broken SU(4)s-wave Tomozawa-Weinberg interaction supplemented by an attractive isoscalar-scalar term. As medium effects, we include Pauli blocking, baryon mean-field bindings, and π and open-charm meson self-energies. The dynamically generated and resonances in the DN sector remain close to their free space position but acquire large widths. The resultant D meson spectral function, which shows a single pronounced quasiparticle peak close to the free mass that broadens with increasing density, also has a long low energy tail associated with smeared , configurations. The low-density approximation for the is questionable already at subsaturation densities. We touch upon the implication of our study for J/Ψ suppression at FAIR.

In the framework of the relativistic mean field theory, the stability of thermal protoneutron stars is investigated. There is a highest possible temperature for a stable protoneutron star. A stable protoneutron star may be a metastable one if its mass is too large. As the temperature increases, the metastable mass range of protoneutron stars narrows. With the increase of temperature, the probability that a stable protoneutron star is a metastable one increases. A really stable protoneutron star with higher temperature can contain more species of hyperons. The case of SN 1987A is analyzed connected with the results in this article.

In this paper, the chiral susceptibility and fermion chiral condensate are investigated in the same framework for Dyson–Schwinger equation. We show that, with the rise of temperature, the susceptibility gives a sharp peak where the chiral symmetry restores. The appearance of the peak and restoration at the same temperature suggests that the peak of chiral susceptibility can be treated as the hint for the restoration of chiral phase transition with the increasing temperature.

In this paper, using the imaginary-time temperature field theory, we discuss the possible modification of chiral anomaly of a massless fermion in (3+1)-dimensional QED (QED₄) when the temperature and chemical potential effects are included. It is found that the chiral anomaly is independent of the temperature and chemical potential. Meanwhile, we also introduce the chemical potential corresponding to chiral charge, and find that it will induce a Chern–Simons-like term, which has similar C transformation properties (and opposite P transformation property) to the corresponding Chern–Simons term in (2+1)-dimensional QED (QED₃). More importantly, we find that when the chemical potential corresponding to the fermion number is space-dependent, it will induce an extra anomaly term. It is expected that this can yield new physical effects.

In this paper, we calculate the effective action for neutral particles with anomalous magnetic moment in an external magnetic and electric field. We show that we can take advantage from the Foldy–Wouthuysen transformation (FWT) for such systems, determined in our previous works: indeed, by this transformation we have explicitly evaluated the diagonalized Hamiltonian, allowing to present a closed form for the corresponding effective action and for the partition function at finite temperature from which the thermodynamical potentials can be calculated.

The temperature dependence of the sum of the QCD up- and down-quark masses, (m_u+m_d) and the pion decay constant, f${}_{\pi }$, are determined from two thermal finite energy QCD sum rules for the pseudoscalar-current correlator. This quark mass remains mostly constant for temperatures well below the critical temperature for deconfinement/chiral-symmetry restoration. As this critical temperature is approached, the quark mass increases sharply with increasing temperature. This increase is far more pronounced if the temperature dependence of the pion mass (determined independently from other methods) is taken into account. The behavior of f${}_{\pi }$(T) is consistent with the expectation from chiral symmetry, i.e. that it should follow the thermal dependence of the quark condensate, independently of the quark mass.

We calculate finite temperature corrections to the energy of the Casimir effect of a two conducting parallel plates in a general weak gravitational field. After solving the Klein–Gordon equation inside the apparatus, mode frequencies inside the apparatus are obtained in terms of the parameters of the weak background. Using Matsubara’s approach to quantum statistical mechanics gravity-induced thermal corrections of the energy density are obtained. Well-known weak static and stationary gravitational fields are analyzed and it is found that in the low temperature limit the energy of the system increases compared to that in the zero temperature case.

Gravitoelectromagnetism (GEM) is an approach for the gravitation field that is described using the formulation and terminology similar to that of electromagnetism. The Lorentz violation is considered in the formulation of GEM that is covariant in its form. In practice, such a small violation of the Lorentz symmetry may be expected in a unified theory at very high energy. In this paper, a non-minimal coupling term, which exhibits Lorentz violation, is added as a new term in the covariant form. The differential cross-section for Bhabha scattering in the GEM framework at finite temperature is calculated that includes Lorentz violation. The Thermo Field Dynamics (TFD) formalism is used to calculate the total differential cross-section at finite temperature. The contribution due to Lorentz violation is isolated from the total cross-section. It is found to be small in magnitude.

In this paper, we investigate the thermal effect on the Casimir energy associated with a massive scalar quantum field confined between two large parallel plates in a CPT-even, aether-like Lorentz-breaking scalar field theory. In order to do that, we consider a nonzero chemical potential for the scalar field assumed to be in thermal equilibrium at some finite temperature. The calculations of the energies are developed by using the Abel–Plana summation formula, and the corresponding results are analyzed in several asymptotic regimes of the parameters of the system, like mass, separations between the plates and temperature.

Gravitoelectromagnetism (GEM) is a gravitational theory similar to electromagnetism. The GEM Lagrangian formalism is used to consider a study of the Cherenkov radiation. This allows us to consider the interaction between gravitons and particles that are fermions. The Thermo Field Dynamics (TFD) formalism is used to introduce the temperature effects. The production rate for Cherenkov radiation at finite temperature is calculated.

A formal analogy between the gravitational and the electromagnetic fields leads to the notion of Gravitoelectromagnetism (GEM) to describe gravitation. A Lagrangian formulation for GEM is developed for scattering processes with gravitons as an intermediate state, in addition to photons for electromagnetic scattering. The differential cross section is calculated for gravitational Möller scattering based on GEM theory. This gravitational cross section is obtained for cases where the Lorentz symmetry is maintained or violated. The Lorentz violation is introduced with the non-minimal coupling term. In addition, using the Thermo Field Dynamics formalism, thermal corrections to the differential cross section are investigated. By comparing the electromagnetic and GEM versions, of Möller scattering, it is shown that the gravitational effect may be measured at an appropriate energy scale.

The pion and kaon properties in a nuclear medium at nonvanishing temperature as well as the quantum chromodynamics (QCD) chiral condensate in the presence of a magnetic field for various baryon densities are studied in the Nambu–Jona–Lasinio (NJL) model with the help of the proper-time regularization (PTR) scheme, simulating a QCD confinement. The density dependence of the quark mass in symmetric nuclear matter is obtained from the quark-meson coupling (QMC) model, which shares the same covariant feature with the NJL model, at quark level. We then analyze the QCD chiral condensates and dynamical masses for various baryon densities at finite temperature and magnetic field as well as the pion and kaon masses, pion and kaon weak-decay constants, pion- and kaon-quark coupling constants, and wave function renormalization factors for various baryon densities at finite temperature. We find that the QCD chiral condensates suppress with increasing temperature and baryon density and enhance under the presence of a magnetic field, which are consistent with other model predictions. Interestingly, the wave function renormalization factors for the pion and kaon increase with respect to temperature and reduce as the baryon density increases are found.