Related papers: Reformulation of Quantum Theory

Reformulation of Quantum Theory

URL: http://arxiv.org/abs/2201.01187v1
Date: Mon, 3 Jan 2022 17:15:35 GMT
Title: Reformulation of Quantum Theory
Authors: Seyed Ebrahim Akrami
Abstract summary: The standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert space as a linear real manifold equipped with its canonical symplectic form and restricting only to the expectation-value functions of Hermitian operators. We reformulate the structure of quantum mechanics in the language of symplectic manifold and avoid linear structure of Hilbert space in such a way that the results can be stated for an arbitrary symplectic manifold.
Score: 0.0
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
Abstract: We first recall a fact which is well-known among mathematical physicists although lesser-known among theoretical physicists that the standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert space as a linear real manifold equipped with its canonical symplectic form and restricting only to the expectation-value functions of Hermitian operators. Then in this framework, we reformulate the structure of quantum mechanics in the language of symplectic manifolds and avoid linear structure of Hilbert space in such a way that the results can be stated for an arbitrary symplectic manifold.

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