Galilean invariance and magnetic charge

Abstract

The Galilean and 'dual' invariant electrodynamics with magnetic charges is formulated. The definition of the main feature of relativistic electromagnetism is given. Consideration of different aspects of Galilean electromagnetism with magnetic charges is presented. It is shown in particular that the conclusion of Bacry & Kubar-Andre (1973) that the existence of the magnetic monopole is incompatible with Galilean invariance in general appears to be incorrect. There jq (jg) is the density of electric (magnetic) current, pq (pg) is the density of electric (magnetic) charge, (cp, j) is a current four-vector, jq = £iJqi, Jg = £iJgi, Oq = ~iPqi, Pg = £i Pgi and subscript (i) indicates a dual charged particles with charges qi and gi, and eo/a o (two constants) are defined in the usual way.Postal address: Dr. V. I. Strazhev,

Newton–Cartan, Galileo–Maxwell and Kaluza–Klein

“…We will be interested in the extension to an arbitrary Newton-Cartan background, which was first performed in [3]. Some aspects of the inclusion of magnetic charge were discussed in [42]. For a clear discussion of the motivations and applications of nonrelativistic electromagnetism we refer to [40].…”

Chiral (γ5) symmetry of massless fields and neutrino theory of photons

“…It is enough to remember about the role of 7s symmetry in the construction of the theory of weak interactions. The consideration of the dual symmetry in the presence of charged particles also leads to interesting results (see, for example, Tomilchik 1973, 1975). The question about the local chiral (Ts) transformations should be paid attention to.…”

“…In this case the law of conservation of some quantity can be found. In the case under consideration the conserved quantity (dual "current") has the following form (Strazhev, 1968(Strazhev, , 1970; see also Strazhev and Tomilchik, 1973):…”