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

Abstract

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.

Inverse magneto-rotational catalysis and the phase diagram of a rotating hot and magnetized quark matter

“…8(a), the T dependence of the constituent mass m is plotted for fixed α b = 10, x = 5 and RΩ = 0.5, and two different choices of GΛ 2 = 24 and GΛ 2 = 26. 10 As expected, for fixed α b , RΩ and T , m increases with increasing GΛ 2 . The same is also true for the critical temperature T c .…”

“…Another important feature of noncentral HICs is the generation of very strong magnetic fields, which has many exciting effects on the Quark matter created in these collisions [3,8,9]. These effects, including the (inverse) magnetic catalysis (see [10] and the references therein) and the chiral magnetic effect [11], are the subject of intensive studies in recent years. In particular, the impact of a constant magnetic field on the QCD phase diagram is studied intensively in the literature [7,12].…”

Chiral anomalous processes in magnetospheres of pulsars and black holes

“…(For reviews, see Refs. [6][7][8][9][10].) Before discussing any physics implications of the anomalous continuity relation (3) in relativistic plasmas, it is instructive to recall that none of the known Dirac particles are truly massless.…”

“…Over the last decade, investigations of the chiral anomalous phenomena in relativistic plasmas attracted much attention. The main applications were focused on the anomalous effects in the quark-gluon plasma produced in heavy-ion collisions [1][2][3][4][5][6][7][8][9][10], hot plasma in the early Universe [11][12][13][14][15][16][17][18], and quasirelativistic electron plasma in Dirac/Weyl semimetals [19,20]. Since relativistic plasmas and strong electromagnetic fields are widespread in astrophysics, it is also sensible to explore the role of anomalous effects there.…”

Polarization tensor of magnetized quark-gluon plasma at nonzero baryon density

“…In a mixed coordinate-momentum space representation, the translation invariant part of the quark propagator Ḡf is given by [28]:…”