monopoles

Monopoles are hypothetical particles or quasiparticles that carry a net magnetic charge, acting as sources or sinks of magnetic field lines. In classical electromagnetism, magnetic field lines form closed loops and there is no magnetic charge density. A true magnetic monopole would modify Maxwell's equations by introducing a magnetic charge density and current, yielding a symmetric set of equations between electric and magnetic fields.

Dirac showed that the existence of even a single monopole would make electric charge appear quantized: the product of electric and magnetic charges must be an integer multiple of ħc/2, establishing a fundamental link between charge units. In non-Abelian gauge theories with spontaneous symmetry breaking, finite-energy monopole solutions were found (the 't Hooft–Polyakov monopole). In grand unified theories, monopoles are predicted to be very massive, potentially around 10^16 GeV, and stabilized by topology.

Cosmological models predict copious production of monopoles during early-universe phase transitions, leading to the monopole problem, later addressed by cosmic inflation which would dilute their abundance. Experimental searches have not found monopoles; numerous detectors have set stringent upper limits on their flux and properties across a range of speeds and masses.

In addition to fundamental monopoles, condensed-matter systems host emergent magnetic monopoles as quasiparticles, notably in spin ice materials, where excitations behave as effective magnetic charges and can move as defects in the spin network.

Today monopoles remain hypothetical in particle physics, but they continue to influence theoretical work and experimental searches, offering insights into charge quantization, dualities in field theory, and the possible structure of fundamental interactions.