A Geometrical Description of Quantum Mechanics

Giuseppe Marmo, G. F. Volkert

In this paper, we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum framework. We apply this formulation to the study of separability and entanglement for states of composite quantum systems.

Nicole Bryant

J. Anandan

José F. Cariñena, Alberto Ibort, G. Marmo +4 more

Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to quantum mechanics. We will concentrate our attention into quantum theories and we will show how to use in a systematic way the transition from algebraic to geometrical structures to explore their geometry, mainly its Jordan‐Lie structure.

J. Anandan

Jesús Clemente-Gallardo, Giuseppe Marmo

Relevant algebraic structures for the description of Quantum Mechanics in the Heisenberg picture are replaced by tensorfields on the space of states. This replacement introduces a differential geometric point of view which allows for a covariant formulation of quantum mechanics under the full diffeomorphism group.