{
  "id": "1301.0885",
  "version": "v2",
  "published": "2013-01-05T09:42:24.000Z",
  "updated": "2014-08-20T06:20:12.000Z",
  "title": "Quantum mechanics revisited",
  "authors": [
    "Jean Claude Dutailly"
  ],
  "comment": "55 pages - 2nd version",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a 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 the eigen value of the operator and appear with the usual probability. Furthermore an equivalent of the Wigner's theorem holds, which leads to the Schr\\\"{o}dinger equation. These results are based on well known mathematics, and do not involve any specific hypothesis in Physics. They validate and explain the methods currently used, which are made simpler and safer, and open new developments. In the second edition of this paper important developments have been added about interacting systems and the transitions of phases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-05T09:42:24.000Z",
      "title": "Quantum Mechanics Revisited",
      "abstract": "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 Schr\\\"odinger 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.",
      "comment": "65 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-08-20T06:20:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum mechanics",
      "usual probability law",
      "wigners theorem holds",
      "general relativity context",
      "hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}