Article

# Dirac monopole with Feynman brackets

Physics Letters A (Impact Factor: 1.63). 04/2000; DOI: 10.1016/S0375-9601(99)00016-X

Source: arXiv

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**ABSTRACT:**In 1992, Dyson published Feynman’s proof of the homogeneous Maxwell equations assuming only the Newton’s law of motion and the commutation relations between position and velocity for a nonrelativistic particle. Recently Tanimura gave a generalization of this proof in a relativistic context. Using the Hodge duality we extend his approach in order to derive the two groups of Maxwell equations with a magnetic monopole in flat and curved spaces. © 1999 American Institute of Physics.Journal of Mathematical Physics 07/1999; 40(8):3732-3737. · 1.30 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Although Maxwell theory is O(3,1)-covariant, electrodynamics only transforms invariantly between Lorentz frames for special forms of the field, and the generator of Lorentz transformations is not generally conserved. Bérard, Grandati, Lages, and Mohrbach have studied the O(3) subgroup, for which they found an extension of the rotation generator that satisfies the canonical angular momentum algebra in the presence of certain Maxwell fields, and is conserved by the classical motion. The extended generator depends on the field strength, but not the potential, and so is manifestly gauge invariant. The conditions imposed on the Maxwell field by the algebra lead to a Dirac monopole solution. In this paper, we study the generalization of the Bérard, Grandati, Lages and Mohrbach construction to the full Lorentz group in N dimensions. The requirements can be maximally satisfied in a three-dimensional subspace of the full Minkowski space; this subspace can be chosen to describe either an O(3)-invariant space sector, or an O(2,1)-invariant restriction of spacetime. The field solution reduces to the Dirac monopole found in the nonrelativistic case when the O(3)-invariant subspace is selected. When an O(2,1)-invariant subspace is chosen, the field strength can be associated with a Coulomb-like potential of the type A μ(x)=n μ/ρ, where ρ =(x μ x μ)1/2, similar to that used by Horwitz and Arshansky to obtain a covariant generalization of the hydrogen-like bound state. In the presence of these fields, which are determined entirely by symmetry considerations, without reference to a source equation, the extended generator is conserved under classical relativistic system evolution.Foundations of Physics 04/2007; 37(4):597-631. · 1.17 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**A Lagrangian formulation describing the electromagnetic interaction — mediated by topologically massive vector bosons — between charged, spin-½ fermions with an Abelian magnetic monopole in a curved space–time with nonminimal coupling and torsion potential is presented. The covariant field equations are obtained. The issue of coexistence of massive photons and magnetic monopoles is addressed in the present framework. It is found that despite the topological nature of photon mass generation in curved space–time with isotropic dilaton field, the classical field theory describing the nonrelativistic electromagnetic interaction between a point-like electric charge and magnetic monopole is inconsistent.International Journal of Modern Physics A 01/2012; 23(26). · 1.13 Impact Factor

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