Gravitational phase operator and cosmic strings

A quantum equivalence principle is formulated by means of a gravitational phase operator which is an element of the Poincaré group. This is applied to the spinning cosmic string which suggests that it may (but not necessarily) contain gravitational torsion. A new exact solution of the Einstein-Cartan-Sciama-Kibble equations for the gravitational field with torsion is obtained everywhere for a cosmic string with uniform energy density, spin density, and flux. A novel effect due to the quantized gravitational field of the cosmic string on the wave function of a particle outside the string is used to argue that spacetime points are not meaningful in quantum gravity. © 1996 The American Physical Society.