Journeys in spacetime

Sigurdsson, Skúli

doi:10.1007/978-3-0348-8278-1_1

Cited by 6 publications

(2 citation statements)

References 37 publications

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“…. Since the transition ( §2.1) from general relativity to Weyl's first gauge theory (1918, §2) has been amply discussed in Pais (1982), Vizgin (1984), Scholz ( , 1995Scholz ( , 2001aScholz ( , 2004Scholz ( , 2011b, Cao (1997), Hawkins (2000), Coleman & Korté (2001), Sigurdsson (2001), Ryckman (2003aRyckman ( ,b, 2005Ryckman ( , 2009, Penrose (2004) and Afriat (2009), I concentrate on the next step, which took Weyl to his second theory ( §3)-mainly determined by the new undulatory ontology ( §3.1) introduced by Louis de Broglie (1924), Dirac (1925), Schrödinger (1926) and others. Mainly but not wholly: Weyl had every reason to keep the electricity, gravity and abstract gauge structure of his first theory; but now with three ingredients (matter, electricity, gravity), three different gauge relations were possible, two of which (electricity-matter, electricity-gravity) were more plausible than the third (matter-gravity).…”

Section: Introductionmentioning

confidence: 99%

Logic of Gauge

Afriat

2019

Studies in History and Philosophy of Science

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The logic of gauge theory is considered by tracing its development from general relativity to Yang-Mills theory, through Weyl's two gauge theories. A handful of elements-which for want of better terms can be called geometrical justice, matter wave, second clock effect, twice too many energy levels-are enough to produce Weyl's second theory; and from there, all that's needed to reach the Yang-Mills formalism is a non-Abelian structure group (say SU(N )).

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Section: Introductionmentioning

confidence: 99%

Logic of Gauge

Afriat

2019

Studies in History and Philosophy of Science

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“… See Pais 1982; Vizgin 1984, chap. 3;Sigurdsson 2001;Coleman and Korté 2001; Hawkins 2000, chap. 11.2; and Scholz 1995.…”

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Hermann Weyl's Analysis of the “Problem of Space” and the Origin of Gauge Structures

Scholz¹

2004

Sci Context

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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.

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Mathematical Modernism, Goal or Problem? The Opposing Views of Felix Hausdorff and Hermann Weyl

Scholz

2023

Archimedes

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Journeys in spacetime

Cited by 6 publications

References 37 publications

Logic of Gauge

Logic of Gauge

Hermann Weyl's Analysis of the “Problem of Space” and the Origin of Gauge Structures

Mathematical Modernism, Goal or Problem? The Opposing Views of Felix Hausdorff and Hermann Weyl

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