Hermann Weyl's Analysis of the "Problem of Space" and the Origin of Gauge Structures
Bibliographic Data
| ID | 4953312 |
|---|---|
| Authors | Erhard Scholz (0000-0001-6741-808X, corresponding author) |
| Year | 2004 |
| Volume | 17 |
| Issue | 1-2 |
| Pages | 165-197 |
| Publication date | 2004-06-01 |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Science in Context (JOURNAL) |
| Journal identifiers | ISSN: 0269-8897 • E-ISSN: 1474-0664 |
| Publisher | Cambridge University Press (CUP) (PUBLISHER) |
| DOI | 10.1017/s0269889704000080 |
| OpenAlex | W2072942811 |
| Language | EN |
| Citations received | 8 |
Hermann Weyl (1885-1955) was one of the early contributors to the mathematics of general relativity. This article argues that in 1929, for the formulation of a general relativistic framework of the Dirac equation, he both abolished and preserved in modified form the conceptual perspective that he had developed earlier in his "analysis of the problem of space." The ideas of infinitesimal congruence from the early 1920s were aufgehoben (in all senses of the German word) in the general relativistic framework for the Dirac equation. He preserved the central idea of gauge as a "purely infinitesimal" aspect of (internal) symmetries in a group extension schema. With respect to methodology, however, Weyl gave up his earlier preferences for relatively a-priori arguments and tried to incorporate as much empiricism as he could. This signified a clearly expressed empirical turn for him. Moreover, in this step he emphasized that the mathematical objects used for the representation of matter structures stood at the center of the construction, rather than interaction fields which, in the early 1920s, he had considered as more or less derivable from geometrico-philosophical considerations
Algebra over a field · Dirac equation · Epistemology · Gauge theory · General relativity · Infinitesimal · Mathematical analysis · Physics · Pure mathematics · Quantum mechanics · Spacetime · Theoretical physics · History and Theory of Mathematics · Mathematics · Philosophy · Philosophy, Science, and History · Relativity and Gravitational Theory · Mathematical Physics
Becker–Blaschke problem of space
Riemann's and Helmholtz-Lie's problems of space from Weyl's relativistic perspective
Introduction to the special issue Hermann Weyl and the philosophy of the ‘New Physics’
Talking at cross-purposes
The notorious man-in-the-street
Hermann Weyl’s neighborhood
Hermann weyl motivations philosophiques d'un choix Maverik
History of Mathematics and History of Science Reunited
| Citations per year | 0.38 |
|---|---|
| Citation span | 2005 - 2024 (20) |
| Highly cited | No |