Geometry of quantum dynamics in infinite dimension

Abstract

We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional and including a Lagrangian formalism in which self-adjoint (Schroedinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we obtain also results concerning coadjoint orbits of the unitary group in infinite dimension, embedding of the Hilbert projective space of pure states in the unitary group, and an approach to self-adjoint extensions of symmetric relations.

32 pages

References in corpus (2)

• Tangent Lifts of Poisson and Related Structures
• Geometry of quantum systems: density states and entanglement

Cited by in corpus (5)

• Differential geometric aspects of parametric estimation theory for states on finite-dimensional C*-algebras
• Manifolds of classical probability distributions and quantum density operators in infinite dimensions
• A symplectic approach to Schrödinger equations in the infinite-dimensional unbounded setting
• From Classical Trajectories to Quantum Commutation Relations
• Poisson structures in the Banach setting: comparison of different approaches