  Differential properties of Klein-Gordon and electromagnetic fields on the
space-time of a straight cosmic string are studied with the help of methods of
the differential space theory. It is shown that these fields are smooth in the
interior of the cosmic string space-time and that they loose this property at
the singular boundary except for the cosmic string space-times with the
following deficit angles : Delta=2\pi*(1-1/n), n=1,2,... A connection between
smoothness of fields at the conical singularity and the scalar and
electromagnetic conical bremsstrahlung is discussed. It is also argued that the
smoothness assumption of fields at the singularity is equivalent to the Aliev
and Gal'tsov "quantization" condition leading to the above mentioned discrete
spectrum of the deficit angle.
