Magnetic monopole in the loop representation

Abstract

We quantize, within the Loop Representation formalism, the electromagnetic field in the presence of a static magnetic pole. It is found that loop-dependent physical wave functionals acquire a topological dependence on the surfaces bounded by the loop. This fact generalizes what occurs in ordinary quantum mechanics in multiply connected spaces. When Dirac's quantization condition is satisfied, the dependence on the surfaces disappears, together with the influence of the monopole on the quantized electromagnetic field.

Geometric representation of the generator of duality in massless and massivep-form field theories

“…We begin by recalling that the Abelian path space can be described as the set of certain equivalence classes of curves γ in a manifold, which we take as R n [12,11,10,19]. The equivalence relation is given in terms of the so called form factor T i ( x, γ) of the curves…”

“…The purpose of this study is to realize the generators of duality transformations of these models in a geometric representation, in order to get some insight into their geometrical meaning. We begin by recalling that the Abelian path space can be described as the set of certain equivalence classes of curves γ in a manifold, which we take as R n [12,11,10,19]. The equivalence relation is given in terms of the so called form factor T i ( x, γ) of the curves…”

“…The Abelian path-space construction may be extended to the case of p-surfaces (p > 1) (see references [19] for the p = 2 generalization). In these cases the geometric space can be described as a set of equivalence classes of p-surfaces Σ labeled by the p-surface form-factor, which is defined as…”