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arXiv:2201.01187

Reformulation of Quantum Theory

Seyed Ebrahim Akrami

Published Jan 3, 2022• 0 citations
arXivHTMLPDF

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.

DOI
10.48550/arxiv.2201.01187

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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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