The space of signed points and the Self Dual Model

Abstract

We study a generalization of the group of loops based on sets of signed points, instead of paths or loops. This geometrical setting incorporates the kinematical constraints of the Sigma Model, inasmuch as the the group of loops does with the Bianchi identities of Yang-Mills theories. We employ an Abelian version of this construction to quantize the Self-Dual Model, which allows us to relate this theory with that of a massless scalar field obeying non-trivial boundary conditions.

(9 pages)

References in corpus (1)

• Loop representation of charged particles interacting with Maxwell and Chern-Simons fields

Cited by in corpus (2)

• Geometric Representation of the generator of duality in massless and massive $p-$form field theories
• A topological invariant in the context of the loop representation of the massive Kalb-Ramond-Klein-Gordon model