There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

비만아 부모의 돌봄 경험: q 방법론

To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle—the graviton—that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms ‘feeling’ laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials—both Abelian and non-Abelian—in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms.

https://iopscience.iop.org/article/10.1088/0034-4885/77/12/126401/pdf

Light-induced gauge fields for ultracold atoms

We compute the electromagnetic fields generated in heavy-ion collisions by using the HIJING model. Although after averaging over many events only the magnetic field perpendicular to the reaction plane is sizable, we find very strong electric and magnetic fields both parallel and perpendicular to the reaction plane on the event-by-event basis. We study the time evolution and the spatial distribution of these fields. Especially, the electromagnetic response of the quark-gluon plasma can give non-trivial evolution of the electromagnetic fields. The implications of the strong electromagnetic fields on the hadronic observables are also discussed.

Event-by-event generation of electromagnetic fields in heavy-ion collisions

The hot and dense matter generated in heavy-ion collisions may contain domains which are not invariant under P and CP transformations. Moreover, heavy-ion collisions can generate extremely strong magnetic fields as well as electric fields. The interplay between the electromagnetic field and triangle anomaly leads to a number of macroscopic quantum phenomena in these P- and CP-odd domains known as anomalous transports. The purpose of this article is to give a pedagogical review of various properties of the electromagnetic fields, the anomalous transport phenomena, and their experimental signatures in heavy-ion collisions.

https://iopscience.iop.org/article/10.1088/0034-4885/79/7/076302/pdf

Electromagnetic fields and anomalous transports in heavy-ion collisions-a pedagogical review.

We study the event-by-event generation of flow vorticity in the BNL Relativistic Heavy Ion Collider $\mathrm{Au}+\mathrm{Au}$ collisions and CERN Large Hadron Collider $\mathrm{Pb}+\mathrm{Pb}$ collisions by using the hijing model. Different definitions of the vorticity field and velocity field are considered. A variety of properties of the vorticity are explored, including the impact parameter dependence, the collision energy dependence, the spatial distribution, the event-by-event fluctuation of the magnitude and azimuthal direction, and the time evolution. In addition, the spatial distribution of the flow helicity is also studied.

Xu-Guang Huang

Papers

Event-by-event generation of electromagnetic fields in heavy-ion collisions

Electromagnetic fields and anomalous transports in heavy-ion collisions-a pedagogical review.

Vorticity in heavy-ion collisions

Azimuthally fluctuating magnetic field and its impacts on observables in heavy-ion collisions

Fate of spin polarization in a relativistic fluid: An entropy-current analysis