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4 de nov. de 2020 · Algebra of gauge theories. Article 30 May 2020. 1 Introduction. The history of gauge theories begins with General Relativity, which can be regarded as a non-Abelian gauge theory of a special type. To a large extent the other gauge theories emerged in a slow and complicated process gradually from General Relativity.
- Norbert Straumann
- norbert.straumann@gmail.com
- 2020
- Idealism in The Infinitesimal
- Transcendental Phenomenological Idealism and “Symbolic Construction”
- Transcendental-Phenomenological Origins of Gauge Invariance
- From The “Raumproblem” to Lie Groups and Lie Algebras
Following the apt term of Bernard , Weyl’s transcendental metaphysics is an “idealism in the infinitesimal”. It is a modern descendant of Leibniz’s principle of continuity (“natura non facit saltus”) i.e., that all finite changes are to be comprehended as arising through infinitesimal increments acting in sequence.Footnote 1Its modern mathematical ...
Weyl’s injunction to understand the world from its behavior in the infinitely small is an evidential constraint upon a transcendental idealism according to which objects of knowledge (natural science) are constitutedvia a process Weyl termed “symbolic construction”: Readers of Kant’s Transcendental Dialectic (A647/B675) will recognize the passage a...
We have previously argued that reformulation of Einstein’s general relativity (GR) within a “purely infinitesimal geometry” was largely spurred by his philosophical orientation to transcendental phenomenological idealism . The mandate of RZM “to comprehend the sense and the justification of the posit of reality (Wirklichkeitssetzung)” beginning fr...
In a natural development from his 1918 “purely infinitesimal” reformulation of general relativity, Weyl turned to the new “space problem” posed by the variably curved manifolds permitted in Einstein’s theory. In the late 1860s, Helmholtz had characterized the geometry of “space” by a set of conditions termed “free mobility” whereby geometrical quan...
- Thomas Ryckman
- tryckman@stanford.edu
- 2020
2 de sept. de 2009 · In 1918, Weyl proposed such a theory. In Weyl (1918a, 1919a), and in the third edition (1920) of Raum-Zeit-Materie, Weyl presented his ingenious attempt to unify gravitation and electromagnetism by constructing a gauge-invariant geometry (see below), or what he called a purely infinitesimal ‘metric’ geometry.
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.
8 de oct. de 2009 · Most readers of this volume will know that the ancestry of gauge field theories extends back to Hermann Weyl's 1918 theory of ‘gravitation and electricity’. Since papers of Yang and others in the 1970s recovered this lineage from obscurity, considerable interest has been shown, and a few years ago a new English translation of ...
- T. A. Ryckman
- 2003
Hermann Weyl (1929a, 1929b). The invariance of a theory under combined transformations such as (1,a,b,c) is known as a gauge invariance or a gauge symmetry and is a touchstone in the creation of modern gauge theories. The gauge symmetry of Quantum Electrodynamics (QED) is an abelian one, described by the U(1) group.
Hermann Weyl's Space-Time Geometry and the Origin of Gauge Theory 100 Years Ago - NASA/ADS. Straumann, Norbert. One of the major developments of twentieth century physics has been the gradual recognition that a common feature of the known fundamental interactions is their gauge structure.
