The Nambu-Jona-Lasinio model in simple configurations of strong and non-homogeneous magnetic fields

Ragazzon, R.

doi:10.1016/0370-2693(94)90709-9

Cited by 6 publications

(11 citation statements)

References 15 publications

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“…The numerical estimates of Ref. [13] confirm the reliability of (24) up to T w 1. Even for such strong gradients, BeR(y) is very close to B(y).…”

Section: Effective Lagrangiansupporting

confidence: 75%

“…[13], where we discussed the Nambu-Jona-Lasinio model in similar conditions. I n particular, our treatment will exploit a remarkable property of the Dirac equation in the presence of magnetic fields with a constant direction.…”

Section: Introductionmentioning

confidence: 94%

“…To be specific let us consider the configuration discussed in Ref. [13], namely, B, = B, = 0, B, = B(y), with a vector potential given by…”

Section: Effective Lagrangianmentioning

confidence: 99%

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Extending the Euler-Heisenberg Lagrangian to some nonperturbative and inhomogeneous field configurations

Ragazzon

1995

Phys. Rev. D

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In this paper we discuss the Euler-Heisenberg effective Lagrangian in nonperturbative and inhomogeneous field configurations characterized by a strong magnetic field of the form B, = B, = 0, B, = B(x, y). Our treatment exploits some interesting properties of the second-order Dirac Hamiltonian describing the electronic motion in the transverse plane (I, y). In particular, we take advantage of the existence of an energy gap separating the excited states from the lowest-lying modes. The latter are exactly calculable and give the leading nontrivial contribution to the effective Lagrangian. Our results show that the presence of gradients can be accounted for by introducing an effective magnetic field strength defined as the sum of the square moduli of the ground state wave functions. This surprisingly simple conclusion is mainly due to a quantum-mechanical supersymmetry of the problem, that of the second-order Dirac Hamiltonian in the transverse plane (x, y). We recall that the same supersymmetry plays an important role for the spontaneous mass generation in the Nambu-Jona-Lasinio model interacting with an external magnetic field. As a simple application of our effective Lagrangian, we discuss the asymptotic behavior of the dielectric permeability tensor of the vacuum as a function of the external field configuration. No anomalous enhancement of the effective electromagnetic coupling is observed. Implications of this result for the GSI peaks are briefly considered.PACS number(s): 11.15.Tk, 12.20.D~

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“…The numerical estimates of Ref. [13] confirm the reliability of (24) up to T w 1. Even for such strong gradients, BeR(y) is very close to B(y).…”

Section: Effective Lagrangiansupporting

confidence: 75%

Section: Introductionmentioning

confidence: 94%

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Extending the Euler-Heisenberg Lagrangian to some nonperturbative and inhomogeneous field configurations

Ragazzon

1995

Phys. Rev. D

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“…In our case the dynamics of the fermion pairing is essentially a (3 + 1)-dimensional one with a quadratic dependence on the cutoff, to be compared with the previous case in equation (9), where we had a (1 + 1)-dimensional behaviour with only a logarithmic dependence on the cutoff.…”

Section: The Standard Four-quark System In a Constant Magnetic F Ieldmentioning

confidence: 86%

“…The generation of mass via catalysis does however not prevail for arbitrary magnetic field configurations. For instance, it has been demonstrated in [9,10] that the NambuJona-Lasinio (NJL) model [11] minimally coupled to a background magnetic field with variable direction becomes massive only beyond some critical value of the strong coupling constant. In these cases dynamical chiral symmetry breaking corresponds to the standard scenario.…”

Section: Introductionmentioning

confidence: 99%

Effects of Quark Interactions on Dynamical Chiral Symmetry Breaking by a Magnetic Field

Hiller

Osipov

Blin

et al. 2008

SIGMA

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Dynamical chiral symmetry breaking by a magnetic field and multi-quark interactions

et al. 2007

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Catalysis of dynamical symmetry breaking by a constant magnetic field in (3 + 1) dimensions is considered. We use the three flavour NambuJona-Lasinio type model with 't Hooft and eight-quark interaction terms. It is shown that the multi-quark interactions introduce new additional features to this phenomenon: (a) the local minimum of the effective potential catalyzed by the constant magnetic field is smoothed out with increasing strength of the field at the characteristic scale H ∼ 10 19 G, (b) the multi-quark forces generate independently another local minimum associated with a larger dynamical fermion mass. This state may exist even for multi-quark interactions with a subcritical set of couplings, and is globally stable with respect to a further increase of the magnetic field. © 2007 Elsevier B.V. All rights reserved. PACS: 11.30.Rd; 11.30.Qc It has been shown in a series of papers [1][2][3] that in (2 + 1) and (3 + 1) dimensions a constant magnetic field H = 0 catalyzes the dynamical symmetry breaking leading to a fermion mass even at the weakest attractive four-fermion interaction between particles, and the symmetry is not restored at any arbitrarily large H . Soon thereafter it became also clear [4][5][6] that the zero-energy surface of the lowest Landau level (LLL) plays a crucial role in the dynamics of such fermion pairing. It has been found that the dynamics of the fermion pairing in the homogeneous magnetic field is essentially (1 + 1)-dimensional, and a deep analogy of this phenomenon with the dynamics of electron pairing in BCS [7] has been stressed. The generated fermion mass, M dyn , turned out to be much smaller than the Landau gap ∼ √ |eH |. The existence of a zero-energy surface in the spectrum of a Dirac particle is ensured for any homogeneous magnetic field with a fixed direction by a quantum mechanical supersymme-* Corresponding author.E-mail address: osipov@nu.jinr.ru (A.A. Osipov).try of the corresponding second-order Dirac Hamiltonian [8]. This aspect of the phenomenon appears to be a quite exceptional situation and indicates that the dynamical generation of mass is not so universal as one would expect by extrapolating the results obtained for homogeneous or unidirectional [9] magnetic field profiles. For instance, it has been demonstrated by Ragazzon [10] that the Nambu-Jona-Lasinio (NJL) model [11] minimally coupled to a background magnetic field with variable direction does not possess a massive phase until the coupling constant exceeds some critical value. Obviously, in this case one faces the conventional scenario of dynamical chiral symmetry breaking, where the magnetic field does not play an essential role. Conversely, having in mind that homogeneous magnetic fields can act as strong catalysts of chiral symmetry breaking, one might ask what is the effect caused by the strong interaction, when higher order multi-fermion interactions are present. These extensions of the NJL model are well known [12][13][14], for instance, the four-quark U(3) L × U(3) R chiral symmetric Lagr...

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The Nambu-Jona-Lasinio model in simple configurations of strong and non-homogeneous magnetic fields

Cited by 6 publications

References 15 publications

Extending the Euler-Heisenberg Lagrangian to some nonperturbative and inhomogeneous field configurations

Extending the Euler-Heisenberg Lagrangian to some nonperturbative and inhomogeneous field configurations

Effects of Quark Interactions on Dynamical Chiral Symmetry Breaking by a Magnetic Field

Dynamical chiral symmetry breaking by a magnetic field and multi-quark interactions

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