On Chiral Symmetry Breaking in a Constant Magnetic Field in Higher Dimension

Chiral symmetry breaking in the Nambu-Jona-Lasinio model in a constant magnetic field is studied in spacetimes of dimension D > 4. It is shown that a constant magnetic field can be characterized by [(D-1)/2] parameters. For the maximal number of nonzero field parameters, we show that there is an effective reduction of the spacetime dimension for fermions in the infrared region D $\to$ 1 + 1 for even-dimensional spacetimes and D $\to$ 0 + 1 for odd-dimensional spacetimes. Explicit solutions of the gap equation confirm our conclusions.Comment: 11 pages, LaTe

Theory of the Magnetic Catalysis of Chiral Symmetry Breaking in QED

The theory of the magnetic catalysis of chiral symmetry breaking in QED is developed. An approximation for the Schwinger-Dyson equations describing reliably this phenomenon is established, i.e., it is shown that there exists a consistent truncation of those equations in this problem. The equations are solved both analytically and numerically, and the dynamical mass of fermions is determined.Comment: 22 pages, 5 figures, REVTe

Gap generation for Dirac fermions on Lobachevsky plane in a magnetic field

We study symmetry breaking and gap generation for fermions in the 2D space of constant negative curvature (the Lobachevsky plane) in an external covariantly constant magnetic field in a four-fermion model. It is shown that due to the magnetic and negative curvature catalysis phenomena the critical coupling constant is zero and there is a symmetry breaking condensate in the chiral limit even in free theory. We analyze solutions of the gap equation in the cases of zero, weak, and strong magnetic fields. As a byproduct we calculate the density of states and the Hall conductivity for noninteracting fermions that may be relevant for studies of graphene.Comment: 12 pages, no figure

Mass Generation in the Supersymmetric Nambu--Jona--Lasinio Model in an External Magnetic Field

The mass generation in the (3+1)-dimensional supersymmetric Nambu-Jona-Lasinio model in a constant magnetic field is studied. It is shown that the external magnetic field catalyzes chiral symmetry breaking.Comment: LaTeX file, 6 pages. Talk given at the International Seminar dedicated to the memory of Dmitrij Volkov "Supersymmetry and Quantum Field Theory", Kharkov, Ukraine, January 5-7, 199

Nondecoupling phenomena in QED in a magnetic field and noncommutative QED

The dynamics in QED in a strong constant magnetic field and its connection with the noncommutative QED are studied. It is shown that in the regime with the lowest Landau level (LLL) dominance the U(1) gauge symmetry in the fermion determinant is transformed into the noncommutative $U(1)_{nc}$ gauge symmetry. In this regime, the effective action is intimately connected with that in noncommutative QED and the original U(1) gauge Ward identities are broken (the LLL anomaly). On the other hand, it is shown that although a contribution of each of an infinite number of higher Landau levels is suppressed in an infrared region, their cumulative contribution is not (a nondecoupling phenomenon). This leads to a restoration of the original U(1) gauge symmetry in the infrared dynamics. The physics underlying this phenomenon reflects the important role of a boundary dynamics at spatial infinity in this problem.Comment: 7 pages, REVTeX

Quantum Phase Fluctuations Responsible for Pseudogap

The effect of ordering field phase fluctuations on the normal and superconducting properties of a simple 2D model with a local four-fermion attraction is studied. Neglecting the coupling between the spin and charge degrees of freedom an analytical expression has been obtained for the fermion spectral function as a single integral over a simple function. From this we show that, as the temperature increases through the 2D critical temperature and a nontrivial damping for a phase correlator develops, quantum fluctuations fill the gap in the quasiparticle spectrum. Simultaneously the quasiparticle peaks broaden significantly above the critical temperature, resembling the observed pseudogap behavior in high-T_c superconductors.Comment: 5 pages, ReVTeX, 1 EPS figure; final version to appear in Physica

Dynamical Chiral Symmetry Breaking in QED in a Magnetic Field: Toward Exact Results

We describe a (first, to the best of our knowledge) essentially soluble example of dynamical symmetry breaking phenomenon in a 3+1 dimensional gauge theory without fundamental scalar fields: QED in a constant magnetic field.Comment: 4 pages, 1 figure, REVTeX. Final version accepted for publication in Physical Review Letter

Color superconductivity in a strong external magnetic field

We explore the effects of an applied strong external magnetic field in a three flavor massless color superconductor. The long-range component of the B field that penetrates the superconductor enhances some quark condensates, leading to a different condensation pattern. The external field also reduces the flavor symmetries in the system, and thus it changes drastically the corresponding low energy physics. Our considerations are relevant for the study of highly magnetized compact stars.Comment: 4 pages; talk given at Strong and Electroweak Matter (SEWM06), BNL, May 200