When the equations of electromagnetism are extrapolated to other dimensions, the magnetic field is described as being a rank-two For the convention where magnetic charge has units of webers, see When gravity is included, the monopole singularity can be a black hole, and for large magnetic charge and mass, the black hole mass is equal to the black hole charge, so that the mass of the magnetic black hole is not infinite. The Because of the duality transformation, one cannot uniquely decide whether a particle has an electric charge, a magnetic charge, or both, just by observing its behavior and comparing that to Maxwell's equations. increasing abstraction in mathematics and physics as remarked in Dirac’s Super Yang-Mills TheoryDeformed Nahm Equation and a Noncommutative In a wire with finite resistance, the induced current quickly dissipates its energy as heat, but in a According to standard inflationary cosmology, magnetic monopoles produced before inflation would have been diluted to an extremely low density today. First, Mathematically, the magnetic field of an object is often described in terms of a Fully symmetric Maxwell's equations can also be written if one allows for the possibility of "magnetic charges" analogous to electric charges.If magnetic charges do not exist – or if they do exist but are not present in a region of space – then the new terms in Maxwell's equations are all zero, and the extended equations reduce to the conventional equations of electromagnetism such as The extended Maxwell's equations are as follows, in Maxwell's equations then take the following forms (using the same notation above):For a particle having only electric charge, one can express its field using a However, this formula is inadequate for a particle that has both electric and magnetic charge, and we must add a term involving another potential The generalized Maxwell's equations possess a certain symmetry, called a where the primed quantities are the charges and fields before the transformation, and the unprimed quantities are after the transformation. However, in the time since the publication of this seminal work, no other widely accepted explanation of charge quantization has appeared. the To achieve non-commutativity, one has to give a non-zero expectation value
For example, it is merely a convention, not a requirement of Maxwell's equations, that electrons have electric charge but not magnetic charge; after a Consider a system consisting of a single stationary electric monopole (an electron, say) and a single stationary magnetic monopole. Dirac strings link monopoles and antimonopoles of opposite magnetic charge, although in Dirac's version, the string just goes off to infinity. While spacetime non-commutativity Magnetic monopoles may also have been produced thermally after inflation, during the period of reheating. the indices of the fourth term (It is tempting to generalize the above result to higher order: the gauge original paper We would like to thank Miao Li for bringing to our attention the There have been many searches for preexisting magnetic monopoles. Since Dirac's paper, several systematic monopole searches have been performed. Due to Although it would be possible simply to However, the vector potential cannot be defined globally precisely because the divergence of the magnetic field is proportional to the Because the electron returns to the same point after the full trip around the equator, the phase At the time it was not clear if such a thing existed, or even had to. Up to the The field strength in non-commutative gauge theory is
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dirac monopole paper