Magnetic moments and general covariance (Q1065376)

Let M be an ordinary spacetime while H is a subgroup of a Lie group G which may include both geometrical information about spacetime and internal symmetries. Denote by \(P_ H\) the set of the diffeomorphisms which commute with the action of H; \(P_ H\) can be enlarged to a principal bundle \(P_ G\). In Cartan's case, the space G/H is assumed to have the same dimension as M, however the author makes a weaker hypothesis, that is, he imposes a nondegeneracy condition which implies that dim G/H\(\leq \dim M\). Some different cases are mentioned in this paper (e.g. M is a Minkowski space, H the Lorentz group and G the Poincaré group). The case of a Cartan connection and Higgs field is also discussed and here the author obtains Souriau's universal equations. Proofs and results are sometimes not very clear; the author refers many times to other papers.