Chiral symmety breaking in 3-flavor Nambu-Jona Lasinio model in magnetic background

Chatterjee, B.; Mishra, Hari Niwas; Mishra, Amruta

doi:10.1016/j.nuclphysa.2011.06.011

Cited by 6 publications

(5 citation statements)

References 9 publications

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“…In the case of two-component fermions, the effective potential, V 2 is V 2 (σ) = V(σ)/2 where V(σ) is defined in Eqs. (66) and (68). However, the essential new point is that there is no continuous U(2) symmetry (and therefore NG modes) in this case.…”

Section: The Spectrum Of the Collective Excitationsmentioning

confidence: 96%

Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

Miransky,

Shovkovy

2015

Preprint

138

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A range of quantum field theoretical phenomena driven by external magnetic fields and their applications in relativistic systems and quasirelativistic condensed matter ones, such as graphene and Dirac/Weyl semimetals, are reviewed. We start by introducing the underlying physics of the magnetic catalysis. The dimensional reduction of the low-energy dynamics of relativistic fermions in an external magnetic field is explained and its role in catalyzing spontaneous symmetry breaking is emphasized. The general theoretical consideration is supplemented by the analysis of the magnetic catalysis in quantum electrodynamics, chromodynamics and quasirelativistic models relevant for condensed matter physics. By generalizing the ideas of the magnetic catalysis to the case of nonzero density and temperature, we argue that other interesting phenomena take place. The chiral magnetic and chiral separation effects are perhaps the most interesting among them. In addition to the general discussion of the physics underlying chiral magnetic and separation effects, we also review their possible phenomenological implications in heavy-ion collisions and compact stars. We also discuss the application of the magnetic catalysis ideas for the description of the quantum Hall effect in monolayer and bilayer graphene, and conclude that the generalized magnetic catalysis, including both the magnetic catalysis condensates and the quantum Hall ferromagnetic ones, lies at the basis of this phenomenon. We also consider how an external magnetic field affects the underlying physics in a class of three-dimensional quasirelativistic condensed matter systems, Dirac semimetals. While at sufficiently low temperatures and zero density of charge carriers, such semimetals are expected to reveal the regime of the magnetic catalysis, the regime of Weyl semimetals with chiral asymmetry is realized at nonzero density. Finally, we discuss the interplay between relativistic quantum field theories (including quantum electrodynamics and quantum chromodynamics) in a magnetic field and noncommutative field theories, which leads to a new type of the latter, nonlocal noncommutative field theories.

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Section: The Spectrum Of the Collective Excitationsmentioning

confidence: 96%

Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

Miransky,

Shovkovy

2015

Preprint

138

View full text Add to dashboard Cite

show abstract

“…In the case of two-component fermions, the effective potential, (66) and (68). However, the essential new point is that there is no continuous U(2) symmetry (and therefore NG modes) in this case.…”

Section: The Spectrum Of the Collective Excitationsmentioning

confidence: 99%

Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

2015

View full text Add to dashboard Cite

a b s t r a c tA range of quantum field theoretical phenomena driven by external magnetic fields and their applications in relativistic systems and quasirelativistic condensed matter ones, such as graphene and Dirac/Weyl semimetals, are reviewed. We start by introducing the underlying physics of the magnetic catalysis. The dimensional reduction of the low-energy dynamics of relativistic fermions in an external magnetic field is explained and its role in catalyzing spontaneous symmetry breaking is emphasized. The general theoretical consideration is supplemented by the analysis of the magnetic catalysis in quantum electrodynamics, chromodynamics and quasirelativistic models relevant for condensed matter physics. By generalizing the ideas of the magnetic catalysis to the case of nonzero density and temperature, we argue that other interesting phenomena take place. The chiral magnetic and chiral separation effects are perhaps the most interesting among them. In addition to the general discussion of the physics underlying chiral magnetic and separation effects, we also review their possible phenomenological implications in heavy-ion collisions and compact stars. We also discuss the application of the magnetic catalysis ideas for the description of the quantum Hall effect in monolayer and bilayer graphene, and conclude that the generalized magnetic catalysis, including both the magnetic catalysis condensates and the quantum Hall ferromagnetic ones, lies at the basis of this phenomenon. We also consider how an external magnetic field affects the underlying physics in a class of three-dimensional quasirelativistic condensed matter systems, Dirac semimetals. While at sufficiently low temperatures and zero density of charge carriers, such semimetals are expected to reveal the regime of the magnetic catalysis, the regime of Weyl semimetals with chiral asymmetry is realized at nonzero density. Finally, we discuss the interplay between relativistic quantum field theories (including quantum electrodynamics and quantum chromodynamics) in a magnetic field and noncommutative field theories, which leads to a new type of the latter, nonlocal noncommutative field theories.

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“…The model-independent nature of magnetic catalysis was tested in numerous (2 + 1)-and (3 + 1)-dimensional models with local four-fermion interactions [13,130,40,182,192,116,117,80,155,114,132,140,141,55,29,10,56], including models with additional gauge interactions [119], higher dimensional models [84], N = 1 supersymmetric models [42], quark-meson models [8,9], models in curved space [81,79,118] and QED-like gauge theories [101,136,156,157,110,104,51,135,105,53,111,106,5,6,107,163,12,11]. The realization of magnetic catalysis was investigated in chiral pertubation theory [174,32,33] and in QCD [144,…”

Section: Introductionmentioning

confidence: 99%

Magnetic Catalysis: A Review

Shovkovy

2013

Lecture Notes in Physics

170

167

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We give an overview of the magnetic catalysis phenomenon. In the framework of quantum field theory, magnetic catalysis is broadly defined as an enhancement of dynamical symmetry breaking by an external magnetic field. We start from a brief discussion of spontaneous symmetry breaking and the role of a magnetic field in its a dynamics. This is followed by a detailed presentation of the essential features of the phenomenon. In particular, we emphasize that the dimensional reduction plays a profound role in the pairing dynamics in a magnetic field. Using the general nature of underlying physics and its robustness with respect to interaction types and model content, we argue that magnetic catalysis is a universal and modelindependent phenomenon. In support of this claim, we show how magnetic catalysis is realized in various models with short-range and long-range interactions. We argue that the general nature of the phenomenon implies a wide range of potential applications: from certain types of solid state systems to models in cosmology, particle and nuclear physics. We finish the review with general remarks about magnetic catalysis and an outlook for future research.

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Chiral symmety breaking in 3-flavor Nambu-Jona Lasinio model in magnetic background

Cited by 6 publications

References 9 publications

Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

Magnetic Catalysis: A Review

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