Quantization of Interacting Non-Relativistic Open Strings using Extended Objects

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.