Klein-Weyl's program and the ontology of gauge and quantum systems

DOI10.1016/j.shpsb.2017.05.003zbMath1382.81009OpenAlexW2625690754MaRDI QIDQ1705891

Gabriel Catren

Publication date: 19 March 2018

Published in: Studies in History and Philosophy of Science. Part B. Studies in History and Philosophy of Modern Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.shpsb.2017.05.003

zbMATH Keywords

symmetriesquantum mechanicsgeneral relativitygauge theoriesHermann WeylKlein's Erlangen program

Mathematics Subject Classification ID

Philosophy of mathematics (00A30) General and philosophical questions in quantum theory (81P05) Yang-Mills and other gauge theories in quantum field theory (81T13) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Special relativity (83A05) Yang-Mills and other gauge theories in mechanics of particles and systems (70S15) Physics (00A79)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geometric foundations of classical Yang-Mills theory
• Introducing groups into quantum theory (1926--1930)
• On classical and quantum objectivity
• Reduction of symplectic manifolds with symmetry
• Structure of dynamical systems. A symplectic view of physics. Transl. from the French by C. H. Cushman-de Vries. Transl. ed.: R. H. Cushman a. G. M. Tuynman
• The theory of topological commutative groups
• Prehistory of the concept of mathematical structure: isomorphism between group theory, crystallography, and philosophy
• On the relation between gauge and phase symmetries
• Empirical Consequences of Symmetries
• Reflections on Quanta, Symmetries, and Supersymmetries
• Husserlian and Fichtean Leanings: Weyl on Logicism, Intuitionism, and Formalism
• In Ehresmann's footsteps: from Group Geometries to Groupoid Geometries
• Conservation of Isotopic Spin and Isotopic Gauge Invariance
• Surplus Structure from the Standpoint of Transcendental Idealism: The “World Geometries” of Weyl and Eddington
• Dénombrabilité des classes d’équivalences dérivées de variétés algébriques
• Harmonic analysis as the exploitation of symmetry-a historical survey
• Homotopy Type Theory: A synthetic approach to higher equalities
• Geometric foundations of Cartan gauge gravity
• Homotopy Type Theory: Univalent Foundations of Mathematics
• Modeling and Control of Complex Physical Systems
• Higher Topos Theory (AM-170)
• Foundations of Quantum Mechanics
• Quantization and unitary representations

This page was built for publication: Klein-Weyl's program and the ontology of gauge and quantum systems