Angel "Java" Lopez en Blog

Publicado el 24 de Diciembre, 2018, 15:51

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No sabía que el trabajo de von Neumann había sido desarrollado antes de la exposición de Dirac. Leo a Jammer:

The major part of the operator calculus in Hilbert space and, in particular, its spectral theory had been worked out by von Neumann before Paul Adrien Maurice Dirac published in 1930 his famous treatise in which he presented a conceptually most compact and notationally most elegant formalism for quantum mechanics. Even though von Neumann admitted that Dirac's formalism could "scarcely be surpassed in brevity and elegance," he criticized it as deficient in mathematical rigor, especially in view of its extensive use of the (at that time) mathematically unacceptable delta-function. Later, when Laurent Schwartz' theory of distributions made it possible to incorporate Dirac's improper functions into the realm of rigorous mathematics -a classic example of how physics may stimulate the growth of new branches in mathematics- Dirac's formalism seemed not to be assimilable to von Neumann's. Yet due to its immediate intuitability and notational convenience Dirac's formalism not only survived but became the favorite framework for many expositions of the theory. The possibility of assimilating Dirac's formalism with von Neu- mann's approach has recently become the subject of important investigations such as Marlow's presentation of the spectral theory in terms of direct integral decompositions of Hilbert space, Roberts recourse to "rigged" Hilbert spaces as well as the investigations by Hermann and Antoine.

Como escribía ayer, el tema de la función delta de Dirac era el núcleo de la crítica de von Neumann. Jammer menciona a Laurent Schwartz y su teoría de la distribución, donde hizo "acceptable" a la idea original de Dirac. Me encontré con esa teoría en "el Penrose". Ver también:

La utilidad de las matemáticas y Laurent Schwartz
Recordando a Beppo Levi (donde Mario Bunge menciona el trabajo de Schwartz)
John von Neumann y Operadores en Cuántica (donde aparece el origen del libro de von Neumann)

Las ideas de Dirac las estoy desarrollando en la serie:

Teoría de la Transformación de Dirac, un desarrollo moderno (1)

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
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Por ajlopez, en: Ciencia