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We determine generally the spinor Green's function and the twisted spinorGreen's function in an Euclidean space with a conical-type line singularity. Inparticular, in the neighbourhood of the point source, we expree them as a sumof the usual Euclidean spinor Green's functin and a regular term. In fourdimensions, we use these determinations to calculate the vacuum energy densityand the twisted one for a massless spinor field in the spacetime of a straightcosmic string. In the Minkowski spacetime, we determine explicitly the vacuumenergy density for a massive twisted spinor field.Comment: 20 pages, latex, no figure

Euclidean spinor Green’s functions in the space–time of a straight cosmic string