QUANTUM MECHANICS REVISITED
Résumé
From a general study of the relations between models, meaning the set of variables with their mathematical properties, and the measures they represent, a new formalism is developed, which covers the scope of Quantum Mechanics. In this paper we prove that the states of any physical system can be represented in a Hilbert space, that a self-adjoint operator is associated to any observable, that the result of a measure must be an eigen value of the operator and appear with the usual probability law. Furthermore an equivalent of the Wigner's theorem holds, which leads to the demonstration of the Schrödinger equation, still valid in the General Relativity context. These results, which come from mathematical demonstrations, based on general and precise assumptions, do not involve any of the hypotheses about determinism, the role of the observer and other topic usually debated. So the formalism which is presented sustains the usual "axioms" of Quantum Mechanics, but opens new developments, notably by considering localized variables an functions, and sections on vector bundle and their jet extensions.
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