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L. Accardi, Adv. Math. 20, 329 (1976).ADMTA4
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Accardi, L.1
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Some reservations with respect to a fundamental importance of CP were expressed in W. A. Majewski, Fortschr. Phys. 32, 89 (1984).FPYKA6
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Majewski, W.A.1
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85037237835
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Note for math purists: The isomorphism is (Formula presented). (Formula presented) depends on the choice of the basis (Formula presented). Take two different bases. The problem with the Ando-Choi-Arveson map (Formula presented) is that the diagram (Formula presented) is noncommutative
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Note for math purists: The isomorphism is (Formula presented). (Formula presented) depends on the choice of the basis (Formula presented). Take two different bases. The problem with the Ando-Choi-Arveson map (Formula presented) is that the diagram (Formula presented) is noncommutative.
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19
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0000722186
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JMAPAQ
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A formalism of mean-field theories especially useful in the context of this paper was given in P. Bóna, J. Math. Phys. 29, 2223 (1988); JMAPAQ
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J. Math. Phys.
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Bóna, P.1
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J. Math. Phys.P. Bóna30, 2994 (1989).
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Bóna, P.1
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85037200001
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T. Ando and M.-D. Choi, in Aspects of Positivity in Functional Analysis, edited by R. Nagel, U. Schlotterbeck, and B. V. Wolff (North-Holland, Amsterdam, 1986)
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T. Ando and M.-D. Choi, in Aspects of Positivity in Functional Analysis, edited by R. Nagel, U. Schlotterbeck, and B. V. Wolff (North-Holland, Amsterdam, 1986).
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30
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85037201009
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This statement seems to apply to the nonuniqueness of (Formula presented), which is always determined up to a transformation (Formula presented) stabilizing (Formula presented)
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This statement seems to apply to the nonuniqueness of (Formula presented), which is always determined up to a transformation (Formula presented) stabilizing (Formula presented), see [15,32].
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33
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0041795644
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World Scientific, Singapore
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M. Czachor and M. Kuna, in Group21: Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras, Vol. 1, edited by W. Scherer, and P. Nattermann, H.-D. Doebner (World Scientific, Singapore, 1997).
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Czachor, M.1
Kuna, M.2
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37
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85037207854
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this concrete example the dynamics is on coadjoint orbits of, respectively, (Formula presented) (Formula presented), and (Formula presented). Quantum mechanics with mean-field backgrounds, as well as a Jordan-Weinberg-type version of nonlinear quantum mechanics were described in a mathematically precise way in the language of coadjoint orbits in P. Bóna, Comenius University report Ph10-91 (1991). This is probably the first paper where a mathematically and physically correct version of a Lie-Poisson nonlinear quantum mechanics of density matrices was formulated
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In this concrete example the dynamics is on coadjoint orbits of, respectively, (Formula presented) (Formula presented), and (Formula presented). Quantum mechanics with mean-field backgrounds, as well as a Jordan-Weinberg-type version of nonlinear quantum mechanics were described in a mathematically precise way in the language of coadjoint orbits in P. Bóna, Comenius University report Ph10-91 (1991). This is probably the first paper where a mathematically and physically correct version of a Lie-Poisson nonlinear quantum mechanics of density matrices was formulated.
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39
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0009244138
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World Scientific, Singapore
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N. Gisin, in Nonlinear, Deformed and Irreversible Quantum Systems, edited by V. K. Dobrev, and P. Natterman, H.-D. Doebner (World Scientific, Singapore, 1995).
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Gisin, N.1
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Commun. Math. Phys.B. Mielnik37, 221 (1969).
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Mielnik, B.1
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46
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85037183000
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We propose the following methodological principle (“Doebner-Goldin razor”): If you discover an impossibility principle stating that any nonlinear modification of quantum mechanics is impossible, first perform the following test. Take a nonlinearly gauge transformed Schrödinger or Liouville–von Neumann equation. If you use a Doebner-Goldin transformation with the parameter (Formula presented) then the transformed equation will have the ordinary kinetic and potential terms but in addition some nonlinearity will appear. Now use this nonlinear dynamics as an example you tried to rule out by your theorem
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We propose the following methodological principle (“Doebner-Goldin razor”): If you discover an impossibility principle stating that any nonlinear modification of quantum mechanics is impossible, first perform the following test. Take a nonlinearly gauge transformed Schrödinger or Liouville–von Neumann equation. If you use a Doebner-Goldin transformation with the parameter (Formula presented) then the transformed equation will have the ordinary kinetic and potential terms but in addition some nonlinearity will appear. Now use this nonlinear dynamics as an example you tried to rule out by your theorem.
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47
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0039978710
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M. Czachor, Phys. Rev. A 57, R2263 (1998).PLRAAN
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Czachor, M.1
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0009244138
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World Scientific, Singapore
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W. Lücke, in Nonlinear, Deformed, and Irreversible Quantum Systems, edited by V. K. Dobrev, and P. Nattermann, H.-D. Doebner (World Scientific, Singapore, 1995).
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Lücke, W.1
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58
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85037191162
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M. Czachor, e-print quant-ph/9711054.
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Czachor, M.1
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