# Classical Yang?Mills theory in condensed matter physics

@article{Berche2013ClassicalYT, title={Classical Yang?Mills theory in condensed matter physics}, author={Bertrand Berche and Ernesto Medina}, journal={European Journal of Physics}, year={2013}, volume={34}, pages={161-180} }

Gauge field theory approaches have been used extensively in recent times to discuss the physical consequences of spin–orbit interactions in condensed matter physics. An SU(2)×U(1) gauge theory is very naturally borne out and provides an illustrative example of classical Yang–Mills field theory at work. This approach may serve as an exemplification of non-Abelian field theories for students in a general physics curriculum. It allows one to introduce discussions on fundamental ideas like Noether…

## 15 Citations

Yang–Mills physics in spintronics

- Physics
- 2020

Abstract We review briefly the origin of gauge physics as well as their modern manifestations e.g. in Yang–Mills, Aharonov–Bohm, Aharonov–Casher, and the Berry–Pancharatnam effects. Yang–Mills has…

Gauge transformations of spin-orbit interactions in graphene

- Physics
- 2015

Inclusion of spin-dependent interactions in graphene in the vicinity of the Dirac points can be posed in terms of non-Abelian gauge potentials. Such gauge potentials being surrogates of physical…

Gradient expansion of the non-Abelian gauge-covariant Moyal star-product

- Physics
- 2021

Motivated by the recent developments of gauge-covariant methods in the phase-space, a systematic method is presented aiming at the generalisation of the Moyal star-product to a non-Abelian gauge…

Pure gauge spin-orbit couplings

- Physics
- 2017

Abstract.Planar systems with a general linear spin-orbit interaction (SOI) that can be cast in the form of a non-Abelian pure gauge field are investigated using the language of non-Abelian gauge…

Skyrmion–electron interaction in the separated spin-up and spin-down quantum hydrodynamics approach

- Physics
- 2020

The Berry gauge field associated with adiabatic quantum evolution represents a very interesting area of research, especially for the description of non-relativistic fermions coupled to a skyrmion…

Using torsion to manipulate spin currents

- Physics
- 2017

We address the problem of quantum particles moving on a manifold characterised by the presence of torsion along a preferential axis. In fact, such a torsion may be taylored by the presence of a…

Charge and spin current oscillations in a tunnel junction induced by magnetic field pulses

- Physics
- 2016

Abstract Usually, charge and spin transport properties in tunnel junctions are studied in the DC bias regime and/or in the adiabatic regime of time-varying magnetic fields. In this letter, the…

Impurity-induced orbital magnetization in a Rashba electron gas

- PhysicsPhysical Review B
- 2018

We investigate the induced orbital magnetization density in a Rashba electron gas with magnetic impurities. Relying on classical electrodynamics, we obtain this quantity through the bound currents…

Spin current generation and control in carbon nanotubes by combining rotation and magnetic field.

- Medicine, PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2020

The main result is the demonstration that, by suitably combining the applied magnetic field intensity and rotation speed, one can tune one of the currents to zero while keeping the other one finite, giving rise to a spin current generator.

Insights into the orbital magnetism of noncollinear magnetic systems

- Physics, EngineeringNanoScience + Engineering
- 2017

The orbital magnetic moment is usually associated with the relativistic spin-orbit interaction, but recently it has been shown that noncollinear magnetic structures can also be its driving force.…

## References

SHOWING 1-10 OF 71 REFERENCES

Classical Yang-mills theory

- Physics, Mathematics
- 1986

We consider classical Yang-Mills theory with point sources and derive equations of motion for the coupled particle-field system. As an example, we discuss the special case of Yang-Mills theory…

NOETHER'S THEOREM FOR LOCAL GAUGE TRANSFORMATIONS

- Physics
- 1990

The variational methods of classical field theory may be applied to any theory with an action that is invariant under local gauge transformations. What is the significance of the resulting Noether…

Spin superfluidity and spin-orbit gauge symmetry fixing

- Physics
- 2012

The Hamiltonian describing 2D electron gas, in a spin-orbit active medium, can be cast into a consistent non-Abelian gauge field theory leading to a proper definition of the spin current. The…

Gauge field theory approach to spin transport in a 2D electron gas

- Physics
- 2009

We discuss the Pauli Hamiltonian including the spin-orbit interaction within an U(1) x SU(2) gauge theory interpretation, where the gauge symmetry appears to be broken. This interpretation offers new…

Gauge invariance and current algebra in nonrelativistic many body theory

- Physics
- 1993

The main purpose of this paper is to further our theoretical understanding of the fractional quantum Hall effect, in particular of spin effects, in two-dimensional incompressible electron fluids…

Gauge symmetry breaking and topological quantization for the Pauli Hamiltonian

- Physics
- 2008

We discuss the Pauli Hamiltonian within a SU(2) gauge theory interpretation, where the gauge symmetry is broken. This interpretation carries directly over to the structural inversion asymmetric…

Equilibrium spin currents: non-Abelian gauge invariance and color diamagnetism in condensed matter.

- Physics, MedicinePhysical review letters
- 2008

It is shown that a magnetic component of this field inevitably generates diamagnetic color currents which are just the equilibrium spin currents discussed in a condensed matter context, which provide an explicit realization of a non-Abelian Landau diamagnetism.

Quantum field theory

- Physics
- 1956

This book is a modern pedagogic introduction to the ideas and techniques of quantum field theory. After a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian…

Gauge theory: Historical origins and some modern developments

- Physics
- 2000

One of the major developments of twentieth-century physics has been the gradual recognition that a common feature of the known fundamental interactions is their gauge structure. In this article the…

Non-Abelian hydrodynamics and the flow of spin in spin-orbit coupled substances

- Physics
- 2007

Motivated by heavy ion collision experiments, we study the hydrodynamic properties of non-Abelian systems. These issues arise in condensed matter physics in the context of transport of spins in the…