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Open Quantum Systems Decoherence
Geometry of quantum dynamics in infinite dimension
arXiv
Authors: Janusz Grabowski, Marek Kus, Giuseppe Marmo, Tatiana Shulman
Year
2017
Paper ID
25034
Status
Preprint
Abstract Read
~2 min
Abstract Words
79
Citations
N/A
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.
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- This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
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- We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple.
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