Pastorello, Davide (2014) *Geometric Hamiltonian Formulation of Quantum Mechanics.* PhD thesis, University of Trento.

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## Abstract

My PhD thesis is focused on geometric Hamiltonian formulation of Quanum Mechanics and its interplay with standard formulation. The main result is the construction of a general prescription to set up a quantum theory as a classical-like theory where quantum dynamics is given by a Hamiltonian vector field on a complex projective space with Kähler structure. In such geometric framework quantum states are represented by classical-like Liouville densities. After a complete characterization of classical-like observables in a finite-dimensional quantum theory, the observable C*-algebra is described in geometric Hamiltonian terms. In the final part of the work, the classical-like Hamiltonian formulation is applied to the study of composite quantum systems providing a notion of entanglement measure.

Item Type: | Doctoral Thesis (PhD) |
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Doctoral School: | Mathematics |

PhD Cycle: | 17 |

Subjects: | Area 01 - Scienze matematiche e informatiche > MAT/07 FISICA MATEMATICA |

Repository Staff approval on: | 24 Nov 2014 10:01 |

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