Spinning cosmic strings and quantization of energy

It is shown that energy should be quantized if there exist cosmic spinning strings. Quantization of energy arises naturally from the fact that the wave function must be single valued in the gravitational field of a spinning string. This effect arises when the vortexlike vacuum configurations carry constant nonzero angular momentum per unit length. Spinning strings occur naturally in spontaneously broken grand unified theories. A limit on J coming from the upper limit of the photon mass is presented. The analogy with quantization of energy in the presence of gravitational magnetic mass is established. (Author)