Dynamical flavor symmetry breaking by a magnetic field in 2+1 dimensions

Gusynin, V. P.; Miransky, V. A.; Shovkovy, Igor

doi:10.1103/physrevd.52.4718

Cited by 243 publications

(287 citation statements)

References 53 publications

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“…It has been shown that a constant magnetic field acts as a strong catalyst of dynamical chiral symmetry breaking, thus leading to the generation of a fermion mass [1,2]. The physics behind this effect is easy to understand: the motion of a charged particle is restricted to directions perpendicular to the magnetic field and this leads to a dimensional reduction (d → d − 2) in the dynamics of the fermion pairing.…”

Section: Introductionmentioning

confidence: 99%

“…Section 4 is devoted to test our formalism against the well-known results of the local Nambu-JonaLasinio (NJL) model [7], setting the stage for the new results concerning nonlocal kernels in the presence of magnetic fields. In particular, we show how to translate the formulae and results obtained within the present formalism to the ones usually obtained through the use of mean-field techniques [1,2]. This translation is a validation of our formalism.…”

Section: Introductionmentioning

confidence: 99%

“…At this point, it is worth commenting on the question of dynamical symmetry breaking in the presence of the magnetic field [2,6]. This problem is connected with the appearance of a fermion condensate B 0|ψψ|0 B = 0 in the limit where the mass parameter m goes to zero.…”

Section: The Approachmentioning

confidence: 99%

“…During the past few years, the behavior of QCD and, more specifically, the problem of dynamical chiral symmetry breaking in the presence of a strong magnetic field have attracted some attention [1,2,3]. It has been shown that a constant magnetic field acts as a strong catalyst of dynamical chiral symmetry breaking, thus leading to the generation of a fermion mass [1,2].…”

Section: Introductionmentioning

confidence: 99%

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The effect of nonlocal confining kernels on magnetic chiral condensates

Felipe¹,

Marques

Ribeiro

2006

Nuclear Physics A

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The physics of spontaneous chiral symmetry breaking in the case of the simultaneous presence of a magnetic field and a fermionic quartic interaction is discussed for both local and nonlocal kernels in 2+1 and 3+1 dimensions. The approach is based on the use of Valatin-Bogoliubov canonical transformations, which allow, in the absence of fermionic quartic terms, to completely diagonalize the Hamiltonian and construct the vacuum state.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: The Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The effect of nonlocal confining kernels on magnetic chiral condensates

Felipe¹,

Marques

Ribeiro

2006

Nuclear Physics A

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“…Among the most interesting topics in the studies of (2+1)-dimensional theories is the parity and chiral symmetry-breaking. In particular, it has been shown that a background magnetic field can serve as a catalyst for the dynamical symmetry breaking [7,8]. In addition, the background gauge fields give rise to the polarization of the ground state for quantum fields with the generation of various types of quantum numbers [4,9].…”

Section: Introductionmentioning

confidence: 99%

Induced fermionic charge and current densities in two-dimensional rings

2016

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For a massive quantum fermionic field, we investigate the vacuum expectation values (VEVs) of the charge and current densities induced by an external magnetic flux in a two-dimensional circular ring. Both the irreducible representations of the Clifford algebra are considered. On the ring edges the bag (infinite mass) boundary conditions are imposed for the field operator. This leads to the Casimir type effect on the vacuum characteristics. The radial current vanishes. The charge and the azimuthal current are decomposed into the boundary-free and boundary-induced contributions. Both these contributions are odd periodic functions of the magnetic flux with the period equal to the flux quantum. An important feature that distinguishes the VEVs of the charge and current densities from the VEV of the energy density, is their finiteness on the ring edges. The current density is equal to the charge density for the outer edge and has the opposite sign on the inner edge. The VEVs are peaked near the inner edge and, as functions of the field mass, exhibit quite different features for two inequivalent representations of the Clifford algebra. We show that, unlike the VEVs in the boundary-free geometry, the vacuum charge and the current in the ring are continuous functions of the magnetic flux and vanish for half-odd integer values of the flux in units of the flux quantum. Combining the results for two irreducible representations, we also investigate the induced charge and current in parity and time-reversal symmetric models. The corresponding results are applied to graphene rings with the electronic subsystem described in terms of the effective Dirac theory with the energy gap. If the energy gaps for two valleys of the graphene hexagonal lattice are the same, the charge densities corresponding to the separate valleys cancel each other, whereas the azimuthal current is doubled.

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Introduction

Gürsoy¹

2021

SpringerBriefs in Physics

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Dynamical flavor symmetry breaking by a magnetic field in 2+1 dimensions

Cited by 243 publications

References 53 publications

The effect of nonlocal confining kernels on magnetic chiral condensates

The effect of nonlocal confining kernels on magnetic chiral condensates

Induced fermionic charge and current densities in two-dimensional rings

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