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# Gauge Fields in the Theory of Condensed Matter and Helicity Conservation

## M. I. Trukhanova

### Moscow University Physics Bulletin 2020. N 2.

• Article
Annotation

A model of the quantum hydrodynamics of a charged particle in an external electromagnetic field is considered with account for the spin–orbit interaction and the influence of the Zeeman energy. The model is based on the formalism of introducing non-Abelian Yang—Mills gauge fields. It is shown that non-Abelian gauge fields generate forces, that act on the spin and spin current. It is demonstrated that the helicity of a particle moving on the background of such fields, that create forces that depend on the spin of the particle, is not conserved. A twofluid model of quantum hydrodynamics is developed for systems of electrons in spin-up and spin-down states moving against the background of the magnetic structure of a skyrmion with a nontrivial topology. A system of continuity equations, momentum balance, and evolution equations of spin density is constructed, and the helicity conservation for electron fluxes is proved in the framework of the proposed two-fluid model.

Received: 2019 November 23
Approved: 2020 July 2
PACS:
11.10.Ef Lagrangian and Hamiltonian approach
64.10.+h General theory of equations of state and phase equilibria
Rissian citation:
М. И. Труханова.
Вестн. Моск. ун-та. Сер. 3. Физ. Астрон. 2020. № 2. С. 3.
Authors
M. I. Trukhanova
$^1$Department of General Physics, Faculty of Physics, M.V.Lomonosov Moscow State University

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