Quantization of Interacting Non-Relativistic Open Strings using Extended Objects

TL;DR

This paper develops a geometric quantization scheme for non-relativistic charged open strings interacting via a Kalb-Ramond field, revealing that charge quantization is essential for consistency.

Contribution

It introduces a novel geometric representation for quantizing interacting open strings, extending the Loop Representation to include surfaces and lines of Faraday.

Findings

Charge quantization is necessary for a consistent geometric representation.

The model describes open-string interactions through a generalized geometric scheme.

The approach extends the Loop Representation to non-relativistic string systems.

Abstract

Non-relativistic charged open strings coupled with Abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. The model comprises open-strings interacting through a Kalb-Ramond field in four dimensions. It is shown that a consistent geometric-representation can be built using a scheme of ``surfaces and lines of Faraday'', provided that the coupling constant (the ``charge'' of the string) is quantized.