Local phase invariance of the free-particle Schrodinger equation in momentum space

Abstract

The local phase-invariance of the momentum-space Schr\"odinger equation for free-particle has been used to construct quantum kinematics that describes a motion of the particle in external U(1) background gauge field. The gauge structure over the momentum space of the particle is interpreted in terms of helicity and spin carried by the particle. As a by-product an effective one-particle Schr\"odinger equation of motion for the helicity-carrying particle in external potential field is derived. An effect of screening of the external potential is predicted, that can affect quantization and splittings of energy levels of the particle.