We consider a spinor particle in the background spacetime generated by a cosmic string. Some physical effects associated with the non-trivial conical topology of this spacetime are investigated. Topological defects of spacetime can be characterized by a spacetime metric with nu11 RiemannChristoffel curvature tensor everywhere except on the defects, that is, by conic type of curvature singularities. Recent attempts to marry the grand unified theories of particle physics with general relativistic models of the early evolution of the universe have predicted the existente of such topological defects. One example of these topological defects are the cosmic stringsI1] which appear naturally in gauge theories with spontaneous symmetry breaking. Cosmic strings are expected to be created during the phase transitions. Some may still exist and may even be observable; others may have collapsed long ago, and have served as the seeds of the galaxies [112]. Straight cosmic strings are long and exceedingly fine objects. Their thickness is comparable to the Compton wavelength h/m (in units c = 1) of typical particles when the string was formed and their tension were enormous, numerically equal to their linear mass density times the square of the speed of light. The tension, for example, for grand unified strings with mass per unit length on the order of 1 0~~~/ c m would be 1 0~~ dynes. The line element of the spacetime described by an infinite, straight and static cylindrically symmetric cosmic string12], lying along the z-ais, is given by [' ] in a cylindrical coordinate system (t, p, cp, z ) with p 2 O and O 5 cp < 2a, the hypersurface cp = O and cp = 27r being identified. The parameter a is related to the linear mass density p of the string by a = 1 -4p. This metric describes the spacetime which is locally flat (for p # 0) but has conelike singularity at p = O with the angle deficit 81rp. Then, the spacetime around an infinite straight and static cosmic string is locally flat but of course not globally flat; it does not differ from Minkowski spacetime locally, it does differ globally. The local flatness of the spacetime surrounding a straight cosrnic string means that there is no local gravity due to the string. There is no Newtonian gravitational potencial around the string and consequently a particle placed at rest in the spacetime of a cosmic string will not be attracted to it, even though the string may have a linear mass density on the order of 1022g/cm. There is no Newtonian gravitational potential around the string, however we have some very interesting gravitational effects associated with the non-trivial topology of the space-like sections around the cosrnic string. Among these effects, a cosrnic string can act as a gravitational l e n~ [~] and can induce a repulsive force on an electric charge at restc4]. Others effects include pair production by a high energy photon when it is placed in the spacetime around a cosmic stringL5] and a gravitational analog~e [~] of the electromagnetic AharonovBohm effectF7]. Clearly a11 those gravitational effects of a cosmic string are due to global (topological) features of this spacetime. In this paper we study some effects of the global features of the spacetime of a straight cosmic string on a spinor particle. To do this we use the Dirac equation in covariant form. Let us consider a spinor quantum particle imbedded in a classical background gravitational field. Its behavior is described by the covariant Dirac equation where yp(x) are the generalized Dirac matrices and are given in terrns of the standard flat spacetime gammas y(') by the relation where e( (x) are vierbeins defined by the relations a
