User:Sparkyscience/Monopoles
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File:Monopole_SU(2)_vortices.jpg The simplest neutral quadruplet of chiral vortices.[1] Electromagnetism with SU(2) symmetry allows for complex nonlinear phenomena such as topological vortices, known as monopoles.
Magnetic monopoles are emergent quasiparticles that exist if and only if the electromagnetic field has non-trivial topology.[2] Magnetic monopoles conserve magnetism, in an analogous way that electrons and protons conserve electric charge. They can be thought of as a kind of domain wall or topological soliton that occurs when the symmetry of electric-magnetic duality is spontaneously broken. Condensation of magnetic monopoles induces the quantization of electric charge, in an exactly analogous way in the Higgs mechanism will quantize the mass of the electron. They can exhibit rich behaviour not encountered in conventional electromagnetism, and are far less constrained then the symmetry considerations required of a relativistically invariant electromagnetic field.[3]
Electromagnetic particles (e.g. electons, protons etc) described in the standard Maxwell equations, or quantum electrodynamics (QED) form a symmetry group. When a particle is translated into any other position, orientation, speed etc. the value of the particle's charge does not vary and is conserved under what is called a gauge transformation, the magnetisation of the particle is not conserved. By definition, a particle that would conserve magnetic and electric charge, a monopole or dyon, would have to have higher symmetry, monopoles are not allowed to exist in in order for divergence-less solenoidal magnetic fields to exist (i.e. it is a requirement of Gauss's law which states that ∇⋅B = 0). Only electric charge is conserved in symmetry. In order for magnetism to be conserved in particles we must use or higher symmetry groups.[4]