Spin-weighted Green's functions in a conical space

We give an analysis of the spin-weighted Green's functions in a conical space. We apply these results in the case of a straight cosmic string and in the Rindler space in order to determine generally the Euclidean Green's functions for the massless spin-1/2 field and for the electromagnetic field. We give also the corresponding Green's functions at aero temperature. However, except for the scalar field, it seems that these Euclidean Green's functions do not correspond to the thermal Feynman Green's functions.