Spherical Manifold in Quantum Evolution

Abstract

In this paper, the projective geometry is used to describe the features of spherical manifold and discreteness in quantum evolution. As a system evolves in time the state vector changes and it traces out a curve in Hilbert space. Geometrically, the evolution is represented as a closed curve in the projective Hilbert space. In recent times many attempts have been made to describe 'length', 'distance', and 'geometric phases' and also 'parallel transport'and symplectic geometry in various ways in the projective Hilbert space, during quantum evolution. It is shown in this paper that for the quantum evolution in ray space, spherical manifold and features of discreteness can be described geometrically.