Geometry of quantum dynamics in infinite dimension
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2017
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| _version_ | 1866929570711601152 |
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| author | Grabowski, Janusz Kus, Marek Marmo, Giuseppe Shulman, Tatiana |
| author_facet | Grabowski, Janusz Kus, Marek Marmo, Giuseppe Shulman, Tatiana |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1711_06486 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Geometry of quantum dynamics in infinite dimension Grabowski, Janusz Kus, Marek Marmo, Giuseppe Shulman, Tatiana Mathematical Physics Differential Geometry Quantum Physics 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. |
| title | Geometry of quantum dynamics in infinite dimension |
| topic | Mathematical Physics Differential Geometry Quantum Physics |
| url | https://arxiv.org/abs/1711.06486 |