A topological theory of the electromagnetic field

Rañada, Antonio Fernández

doi:10.1007/bf00401864

Cited by 153 publications

(266 citation statements)

References 18 publications

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“…The Hopf fibration can also be used in the construction of finite-energy radiative solutions to Maxwell's equations and linearized Einstein's equations [8]. Some examples are Ranada's null electromagnetic (EM) hopfion [9,10] and its generalization to torus knots [1,11,12].…”

Section: Introductionmentioning

confidence: 99%

Constructing a class of topological solitons in magnetohydrodynamics

et al. 2014

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We present a class of topological plasma configurations characterized by their toroidal and poloidal winding numbers, n t and n p , respectively. The special case of n t = 1 and n p = 1 corresponds to the Kamchatnov-Hopf soliton, a magnetic field configuration everywhere tangent to the fibers of a Hopf fibration so that the field lines are circular, linked exactly once, and form the surfaces of nested tori. We show that for n t ∈ Z + and n p = 1, these configurations represent stable, localized solutions to the magnetohydrodynamic equations for an ideal incompressible fluid with infinite conductivity. Furthermore, we extend our stability analysis by considering a plasma with finite conductivity, and we estimate the soliton lifetime in such a medium as a function of the toroidal winding number.

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Section: Introductionmentioning

confidence: 99%

Constructing a class of topological solitons in magnetohydrodynamics

et al. 2014

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“…Corresponding author E-mail: joseluis.trueba@urjc.es, Phone: +34 91 488 8460 Área de Electromagnetismo, Universidad Rey Juan Carlos, Camino del Molino s/n, 28943 Fuenlabrada, Madrid, Spain electric fields at t = 0 as 2 , whereφ andθ are the complex conjugates of φ and θ respectively, i is the imaginary unit, a is a constant introduced so that the magnetic and electric fields have correct dimensions, and c is the velocity of light in vacuum. In the SI of units, a can be expressed as a pure number times the Planck constant ħ times the light velocity c times the vacuum permeability μ 0 .…”

Section: Construction and Resultsmentioning

confidence: 99%

“…Since these quantities are related to the Gauss linking integral and the self-linking number of the magnetic and the electric lines, respectively, if they are not zero then one can expect that there will be a certain degree of linkage in the lines and this linkage will not disappear in time. Nice particular examples of this case are Rañada electromagnetic knots [1][2][3][4][5][6][7]12] in which, by construction, always satisfy that the electric and magnetic fields are mutually orthogonal. Moreover, in the case of Rañada electromagnetic knots the magnetic helicity is equal to a topological invariant, the Hopf index of a map between the compactified space R 3 and the compactified complex plane, and the electric helicity is equal to the Hopf index of another map between the compactified space R 3 and the compactified complex plane.…”

Section: Consequencesmentioning

confidence: 99%

Exchange of helicity in a knotted electromagnetic field

Arrayás

Trueba

2011

Annalen der Physik

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There are solutions of Maxwell equations in vacuum in which the magnetic and the electric lines have a nontrivial topology. This behaviour has physical consequences since it is related to classical expressions indicating aspects of the photon content of the electromagnetic field. In this work we present for the first time an exact solution of Maxwell equations in vacuum, having non trivial topology, in which there is an exchange of helicity between the electric and magnetic part of such field. We calculate the temporal evolution of the magnetic and electric helicities, and explain the exchange of helicity making use of the Chern-Simon form. We also have found and explained that, as time goes to infinity, both helicities reach the same value and the exchange between the magnetic and electric part of the field stops.

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“…The key to the answer stems from the observation that in the physical world (in which the dispersion integral (14) is written), the theory possesses light quarks of mass m f , and in the chiral limit of massless quarks the correlation function of topological charge in (14) must vanish. This is because at m f = 0 the topological charge is a full divergence of the gauge-invariant axial current (see (8)).…”

Section: Venezianomentioning

confidence: 99%

Color confinement from fluctuating topology

Kharzeev

2016

Int. J. Mod. Phys. A

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QCD possesses a compact gauge group, and this implies a non-trivial topological structure of the vacuum. In this contribution to the Gribov-85 Memorial volume, we first discuss the origin of Gribov copies and their interpretation in terms of fluctuating topology in the QCD vacuum. We then describe the recent work with E. Levin that links the confinement of gluons and color screening to the fluctuating topology, and discuss implications for spin physics, high energy scattering, and the physics of quark-gluon plasma.

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A topological theory of the electromagnetic field

Cited by 153 publications

References 18 publications

Constructing a class of topological solitons in magnetohydrodynamics

Constructing a class of topological solitons in magnetohydrodynamics

Exchange of helicity in a knotted electromagnetic field

Color confinement from fluctuating topology

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