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Register a new userThermodynamics of Chiral Fermion System in a Uniform Magnetic Field
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We construct the grand partition function of the system of chiral fermions in a uniform magnetic field from Landau levels, through which all thermodynamic quantities can be obtained. Taking use of Abel-Plana formula, these thermodynamic quantities can be expanded as series with respect to a dimensionless variable $b=2eB/T^{2}$. We find that the series expansions of energy density, pressure, magnetization intensity and magnetic susceptibility contain a singular term with $ln b^{2}$, while particle number density, entropy density and heat capacity are power series of $b^{2}$. The asymptotic behaviors of these thermodynamic quantities in extreme conditions are also discussed.
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Using the nonperturbative Schwinger-Dyson equation, we show that chiral symmetry is dynamically broken in QED at weak couplings when an external magnetic field is present, and that chiral symmetry is restored at temperatures above $T_c simeq alphapi^2/sqrt{2 pi |eH|}$, where $alpha$ is the fine structure constant and $H$ is the magnetic field strength.
We study chiral symmetry breaking in QED when a uniform external magnetic field is present. We calculate higher order corrections to the dynamically generated fermion mass and find them to be small. In so doing we correct an error in the literature regarding the matrix structure of the fermion self-energy.
We reconsider the problem of calculating the vacuum free energy (density) of QCD and the shift of the quark condensates in the presence of a uniform background magnetic field using two-and-three-flavor chiral perturbation theory ($chi$PT). Using the free energy, we calculate the degenerate, light quark condensates in the two-flavor case and the up, down and strange quark condensates in the three-flavor case. We also use the vacuum free energy to calculate the (renormalized) magnetization of the QCD vacuum, which shows that it is paramagnetic. We find that the three-flavor light-quark condensates and (renormalized) magnetization are improvements on the two-flavor results. We also find that the average light quark condensate is in agreement with the lattice up to $eB=0.2 {rm GeV^{2}}$, and the (renormalized) magnetization is in agreement up to $eB=0.3 {rm GeV^{2}}$, while three-flavor $chi$PT, which gives a non-zero shift in the difference between the light quark condensates unlike two-flavor $chi$PT, underestimates the difference compared to lattice QCD.
We show that the presence of a magnetic monopole in position space gives rise to a violation of the fermion number conservation in chiral matter. Using the chiral kinetic theory, we derive a model-independent expression of such a violation in nonequilibrium many-body systems of chiral fermions. In local thermal equilibrium at finite temperature and chemical potential, in particular, this violation is proportional to the chemical potential with a topologically quantized coefficient. These consequences are due to the interplay between the Dirac monopole in position space and the Berry monopole in momentum space. Our mechanism can be applied to study the roles of magnetic monopoles in the nonequilibrium evolution of the early Universe.
Chiral symmetry is dynamically broken in quenched, ladder QED at weak gauge couplings when an external magnetic field is present. In this paper, we show that chiral symmetry is restored above a critical chemical potential and the corresponding phase transition is of first order. In contrast, the chiral symmetry restoration at high temperatures (and at zero chemical potential) is a second order phase transition.
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