Geometry of projective Hilbert space

1 December 1992

journal article
research article
Published by American Physical Society (APS) in Physical Review A

Vol. 46 (11) , 7292-7294
https://doi.org/10.1103/physreva.46.7292

Abstract

Geodesic equations determined by the metric in a projective Hilbert space openP are found. It is shown that connections in the tangent bundle over openP consistent with these geodesics can be introduced. A connection with zero torsion is proposed. Quantum-system dynamics follows the geodesics of another connection which is found for the case of the constant Hamiltonian. A set of geometrical quantities is defined, conserved by a quantum evolution.

Keywords

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