QUANTUM-MECHANICS OF RELATIVISTIC-PARTICLES IN MULTIPLY CONNECTED SPACES AND THE AHARONOV-BOHM EFFECT

We consider the motion of free relativistic particles in multiply connected spaces. We show that if one of the spatial dimensions has the topology of a circle then the D-dimensional spacetime is compactified to D-1 dimensions and the particle mass increases by an amount which is proportional to a quantum phase factor and inversely proportional to the radius of the circle. This provides a new non-perturbative mechanism of mass generation. We also consider the relativistic Aharanov-Bohm effect and we show that the propagator is similar in form to the non-relativistic one. The propagators are calculated without any approximation in both situations.