The space of signed points and the Self Dual Model

TL;DR

This paper introduces a generalized geometric framework based on signed points to analyze the Self-Dual Model, connecting it to scalar field theories with boundary conditions and extending loop group concepts.

Contribution

It develops a novel geometric approach using signed points to study the Self-Dual Model and relates it to scalar fields with boundary conditions.

Findings

Quantization of the Self-Dual Model using Abelian signed points

Connection established between the model and massless scalar fields with boundary conditions

Extension of loop group concepts to signed point sets

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.