In finite dimension (at least), Quantum Mechanics can be formulated as a proper Hamiltonian theory where a notion of phase space is given by the projective space P(H) constructed on the Hilbert space H of the considered quantum theory. It is well-known P(H) can be equipped with a structure of Kahler manifold, in particular we have a symplectic form and a Poisson structure; Quantum dynamics can be described in terms of a Hamiltonian vector field on P(H). In this paper, exploiting the notion and properties of so-called frame functions, I describe a general prescription for associating quantum observables to real functions on P(H), classical-like observables, and quantum states to probability densities on P(H), Liouville densities, in order to obtain a complete and meaningful Hamiltonian formulation of a finite-dimensional quantum theory.

Pastorello, D. (2015). Geometric Hamiltonian formulation of quantum mechanics in complex projective spaces. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 12(8), 1560015-1-1560015-8 [10.1142/S0219887815600154].

Geometric Hamiltonian formulation of quantum mechanics in complex projective spaces

Pastorello, D
2015

Abstract

In finite dimension (at least), Quantum Mechanics can be formulated as a proper Hamiltonian theory where a notion of phase space is given by the projective space P(H) constructed on the Hilbert space H of the considered quantum theory. It is well-known P(H) can be equipped with a structure of Kahler manifold, in particular we have a symplectic form and a Poisson structure; Quantum dynamics can be described in terms of a Hamiltonian vector field on P(H). In this paper, exploiting the notion and properties of so-called frame functions, I describe a general prescription for associating quantum observables to real functions on P(H), classical-like observables, and quantum states to probability densities on P(H), Liouville densities, in order to obtain a complete and meaningful Hamiltonian formulation of a finite-dimensional quantum theory.
2015
Pastorello, D. (2015). Geometric Hamiltonian formulation of quantum mechanics in complex projective spaces. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 12(8), 1560015-1-1560015-8 [10.1142/S0219887815600154].
Pastorello, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/926044
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