By Dmitri Kharzeev, Karl Landsteiner, Andreas Schmitt, Ho-Ung Yee

The physics of strongly interacting topic in an exterior magnetic box is shortly rising as a subject matter of significant cross-disciplinary curiosity for particle, nuclear, astro- and condensed topic physicists.

It is understood that powerful magnetic fields are created in heavy ion collisions, an perception that has made it attainable to review various extraordinary and fascinating phenomena that emerge from the interaction of quantum anomalies, the topology of non-Abelian gauge fields, and the magnetic box. particularly, the non-trivial topological configurations of the gluon box result in a non-dissipative electrical present within the presence of a magnetic box. those phenomena have resulted in a longer formula of relativistic hydrodynamics, referred to as chiral magnetohydrodynamics.

Hitherto unforeseen purposes in condensed topic physics comprise graphene and topological insulators. different fields of software contain astrophysics, the place robust magnetic fields exist in magnetars and pulsars.

Last yet now not least, a massive new theoretical instrument that might be revisited and which made a lot of the growth surveyed during this e-book attainable is the holographic precept - the correspondence among quantum box thought and gravity in additional dimensions.

Edited and authored by means of the pioneers and top specialists during this newly rising box, this publication deals a helpful source for a wide neighborhood of physicists and graduate students.

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**Strongly Interacting Matter in Magnetic Fields**

The physics of strongly interacting topic in an exterior magnetic box is shortly rising as an issue of significant cross-disciplinary curiosity for particle, nuclear, astro- and condensed topic physicists. it's recognized that robust magnetic fields are created in heavy ion collisions, an perception that has made it attainable to check numerous spectacular and fascinating phenomena that emerge from the interaction of quantum anomalies, the topology of non-Abelian gauge fields, and the magnetic box.

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**Example text**

Is the quantum number associated with the orbital motion in the perpendicular plane. The corresponding normalized wave functions read ψkp2 (r⊥ ) = √ 1 2π 1 √ Hk 2k k! 82) √ where Hk (z) are the Hermite polynomials [94], = 1/ |eB| is the magnetic length, and s⊥ ≡ sign(eB). 84) k=0 −∞ respectively. 81) as follows: ∞ S ω, p ; r⊥ , r⊥ = 3 ∞ i γ 0 ω − (π ⊥ · γ ⊥ ) − γ 3 p 3 + m ω2 − p 3 dp2 −∞ 2 k=0 − (2k + 1)|eB| + ieBγ 1 γ 2 − m2 −1 ∗ r⊥ ψkp2 (r⊥ )ψkp 2 = eiΦ(r⊥ ,r⊥ ) S˜ ω, p 3 ; r⊥ − r⊥ . 90) where we used the short-hand notation ξ= (r⊥ − r⊥ )2 .

40) Λ dk −ikx . 5 Analogy with Superconductivity It is interesting to point that the dynamics described by the gap equation in the case of magnetic catalysis has a lot of conceptual similarities to the mechanism of superconductivity in metals and alloys. This is despite the clear differences between the two phenomena that we discussed in the Introduction. 41) where N(0) is the density of electron states at the Fermi surface, ωD is the Debye frequency, and Δ is the energy gap associated with superconductivity.

A dynamical generation of quark masses spontaneously breaks the chiral symmetry down to SU (Nu )V × SU (Nd )V and gives rise to Nu2 + Nd2 − 1 massless Nambu-Goldstone bosons in the low-energy spectrum. Just like in QED, the vacuum polarization effects play a very important role in QCD in the presence of a strong magnetic field. A. 57) μν where k ≡ g kν and g ≡ diag(1, 0, 0, −1) is the projector onto the longitudinal subspace. Notice that quarks in a strong magnetic field do not couple to the transμν μν μ μν verse subspace spanned by g⊥ ≡ g μν − g = diag(0, −1, −1, 0) and k⊥ ≡ g⊥ kν .