Angel "Java" Lopez en Blog

Publicado el 9 de Noviembre, 2014, 13:26

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Estuve leyendo estos días más sobre la historia de vida de Heisenberg. Uno de los libros que leyó antes de entrar a la universidad, fue un clásico de Hermann Weyl, Espacio, Tiempo y Materia. Hoy fui a leer las primeras secciones, y me encuentro con Weyl comentando sobre una teoría gauge suya, que no tuvo éxito. Escribe en el prefacio a la primera edición americana:

This translation is made from the fourth edition of raum zkit matkrik which was published in 1921. Relativity theory as expounded in this book deals with the space-time aspect of classical physics. Thus, the book's contents are comparatively little affected by the stormy development of quantum physics during the last three decades. This fact, aside from the public's demand, may justify its re-issue after so long a time. Of course, had the author to re-write the book today, he would take into account certain events that have modified the situation in the intervening years.

Weyl menciona como primer punto el tema que nos interesa: su primer teoría gauge:

The principle of general relativity had resulted above all in a new theory of the gravitational field. While it was not difficult to adapt also Maxwell's equations of the electromagnetic field to this principle, it proved insufficient to reach the goal at which classical field physics is aiming: a unified field theory deriving all forces of nature from one common structure of the world and one uniquely determined law of action. In the last two of its 36 sections, my book describes an attempt to attain this goal by a new principle which I called gauge invariance (Eichinvarianz). This attempt has failed. There holds, as we know now, a principle of gauge invariance in nature; but it does not connect the electromagnetic potentials phi i, as I had assumed, with Einstein's gravitational potentials gik , but ties them to the four components of the wave field psi by which Schrodinger and Dirac taught us to represent the electron. For this and the following points, compare my book, gruppentheorie und quantenmechanik, Leipzig 1928, 2nd ed. 1931, the article, "Elektron und Gravitation" in Zeilschr. f. Physik 56, 1929, p. 330, and my Rouse Ball lecture "Geometry and Physics" in Naturwissenschaflen 19, 1931, pp. 49-58. Of course, one could not have guessed this before the "electronic field" Psi was discovered by quantum mechanics! Since then, however, a unitary field theory, so it seems to me, should encompass at least these three fields: electromagnetic, gravitational and electronic. Ultimately the wave fields of other elementary particles will have to be included too—unless quantum physics succeeds in interpreting them all as different quantum states of one particle.

El psi que menciona es la función de onda de Schrödinger. La primera noticia de este intento gauge de Weyl la encontré en el Penrose. Esto de arriba lo escribe Weyl ya en 1950, sobre la versión de su libro de 1921, y es interesante ver cómo esa idea que no funcionó, luego tuvo su aplicación y resurgimiento en la teoría cuántica, en la función de onda que se introdujo pudo aplicar un cambio de fase complejo.

Leo en artículo de la Wikipedia sobre Weyl:

Weyl, as a major figure in the Göttingen school, was fully apprised of Einstein's work from its early days. He tracked the development ofrelativity physics in his Raum, Zeit, Materie (Space, Time, Matter) from 1918, reaching a 4th edition in 1922. In 1918, he introduced the notion of gauge, and gave the first example of what is now known as a gauge theory. Weyl's gauge theory was an unsuccessful attempt to model the electromagnetic field and the gravitational field as geometrical properties of spacetime. The Weyl tensor in Riemannian geometry is of major importance in understanding the nature of conformal geometry. In 1929, Weyl introduced the concept of the vierbeininto general relativity.[9]

Más sobre las ideas de Weyl en la sección 3 de On the Origins of Gauge Theory.

Ya mencioné a Hermann Weyl en:

Hermann Weyl, Teoría de Grupos y Teoría Cuántica
Hermann Weyl, fisica y matemáticas
Notas sobre Invariantes (1)
Paul Adrien Maurice Dirac por Abraham Pais (8)
Física Cuántica (Parte 3) Vectores de Estado y Realidad Física
Números Complejos en Mecánica Cuántica (1)
Grupos y Física, por Dirac
Estudiando Física Cuántica (1)

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Angel "Java" Lopez
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Por ajlopez, en: Ciencia