Statistical transmutation of quantum bosonic strings coupled to general four-dimensional Chern-Simons theory

A bosonic string coupled to the generalized Chern-Simons theory in 3+1D acquires a magnetic field along itself, when it is closed, and a topological charge at its extremity, when it is open. We construct the creation operators for the full quantum field states associated to these strings and determine the dual algebra satisfied by them. We show that the creation operator fo the composite state of a quantum closed bosonic string, bearing a magnetic flux, and a topologically charged open bosonic string, possesses generalized statistics. The relation of our results with previous approaches to the problem is also established.Comment: 4 pages, Revtex

Fractional Statistics in Three Dimensions: Compact Maxwell-Higgs System

We show that a (3+1)-dimensional system composed of an open magnetic vortex and an electrical point charge exhibits the phenomenon of Fermi-Bose transmutation. In order to provide the physical realization of this system we focus on the lattice compact scalar electrodynamics $SQED_c$ whose topological excitations are open Nielsen-Olesen strings with magnetic monopoles attached at their ends.Comment: 8 page

A Geometric Approach to Massive p-form Duality

Massive theories of abelian p-forms are quantized in a generalized path-representation that leads to a description of the phase space in terms of a pair of dual non-local operators analogous to the Wilson Loop and the 't Hooft disorder operators. Special atention is devoted to the study of the duality between the Topologically Massive and the Self-Dual models in 2+1 dimensions. It is shown that these models share a geometric representation in which just one non local operator suffices to describe the observables.Comment: 26 pages, LaTeX. The discussion about the equivalence between the Proca model and two seldual models, with opposite spins, was eliminated. Typos correcte

Interacting Particles and Strings in Path and Surface Representations

Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models: the string in self-interaction through a Kalb-Ramond field in four dimensions, the topological interaction of two particles due to a BF term in 2+1 dimensions, and the string-particle interaction mediated by a BF term in 3+1 dimensions. In the first case one finds that a consistent "surface-representation" can be built provided that the coupling constant is quantized. The geometrical setting that arises corresponds to a generalized version of the Faraday's lines picture: quantum states are labeled by the shape of the string, from which emanate "Faraday`s surfaces". In the other models, the topological interaction can also be described by geometrical means. It is shown that the open-path (or open-surface) dependence carried by the wave functional in these models can be eliminated through an unitary transformation, except by a remaining dependence on the boundary of the path (or surface). These feature is closely related to the presence of anomalous statistics in the 2+1 model, and to a generalized "anyonic behavior" of the string in the other case.Comment: RevTeX 4, 28 page

The Extended Loop Group: An Infinite Dimensional Manifold Associated with the Loop Space

A set of coordinates in the non parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of these objects is proposed. The enlarged group behaves locally as an infinite dimensional Lie group. Ordinary loops form a subgroup of this group. The algebraic properties of this new mathematical structure are analized in detail. Applications of the formalism to field theory, quantum gravity and knot theory are considered.Comment: The resubmited paper contains the title and abstract, that were omitted in the previous version. 42 pages, report IFFI/93.0

Non Abelian BF theories with sources and 2-D gravity

We study the interaction of non-Abelian topological $BF$ theories defined on two dimensional manifolds with point sources carrying non-Abelian charges. We identify the most general solution for the field equations on simply and multiply connected two-manifolds. Taking the particular choice of the so-called extended Poincar\'e group as the gauge group we discuss how recent discussions of two dimensional gravity models do fit in this formalism.Comment: 20 pages, Latex, To appear in Phys Rev D5

Fermionic String from Abelian Higgs Model with monopoles and Θ\Theta-term

The four dimensional Abelian Higgs model with monopoles and $\Theta$-term is considered in the limit of the large mass of the higgs boson. We show that for $\Theta=2 \pi$ the theory is equivalent, at large distances, to summation over all possible world-sheets of fermionic strings with Dirichlet type boundary conditions on string coordinates.Comment: 8 pages, LaTeX file, no figures. Submitted to JETP Let