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Abstract:

Our aim in this paper is to take quite seriously Heinz Post's claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller's words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. We build a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg's suggestion that new phenomena require the formation of a new "closed" (that is, axiomatic) theory, coping also with the physical theory's underlying logic and mathematics. © 2008 Springer Science+Business Media, LLC.

Registro:

Documento: Artículo
Título:Q-spaces and the foundations of quantum mechanics
Autor:Domenech, G.; Holik, F.; Krause, D.
Filiación:Instituto de Astronomía y Física Del Espacio (IAFE), Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires, Argentina
Departamento de Filosofia, Universidade Federal de Santa Catarina, P.O. Box 476, Forianópolis, SC 88040-900, Brazil
Palabras clave:Fock space; Particle number; Quantum indistinguishability; Quasi-sets
Año:2008
Volumen:38
Número:11
Página de inicio:969
Página de fin:994
DOI: http://dx.doi.org/10.1007/s10701-008-9246-9
Título revista:Foundations of Physics
Título revista abreviado:Found. Phys.
ISSN:00159018
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00159018_v38_n11_p969_Domenech

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Citas:

---------- APA ----------
Domenech, G., Holik, F. & Krause, D. (2008) . Q-spaces and the foundations of quantum mechanics. Foundations of Physics, 38(11), 969-994.
http://dx.doi.org/10.1007/s10701-008-9246-9
---------- CHICAGO ----------
Domenech, G., Holik, F., Krause, D. "Q-spaces and the foundations of quantum mechanics" . Foundations of Physics 38, no. 11 (2008) : 969-994.
http://dx.doi.org/10.1007/s10701-008-9246-9
---------- MLA ----------
Domenech, G., Holik, F., Krause, D. "Q-spaces and the foundations of quantum mechanics" . Foundations of Physics, vol. 38, no. 11, 2008, pp. 969-994.
http://dx.doi.org/10.1007/s10701-008-9246-9
---------- VANCOUVER ----------
Domenech, G., Holik, F., Krause, D. Q-spaces and the foundations of quantum mechanics. Found. Phys. 2008;38(11):969-994.
http://dx.doi.org/10.1007/s10701-008-9246-9