Differential Structure of Space-Time and Physical Fields

Abstract

A physical interpretation of axioms of the differential structure of space-time is presented. Consequences of such interpretation for cosmic string's space-time with a scalar field are studied. It is shown that the assumption of smoothness of the scalar field leads either to modification of cosmic string's space-time global properties or to quantization of the deficit of angle: $\Delta =2\pi (1-1/n)$, $n=1,2,\dots$.Comment: 9 pages, LaTeX, Lecture delivered at " Workshop on Modern Methods in Classical and Quantum Gravity ", July 26-28th, 1995, Sintra, Portuga