2013/10/28 by Erhard Scholz, Scholz, Erhard
Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #History and Overview (math.HO) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1310.7334
openalex publication_date 2013/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Starting from a short review of the "classical" space problem in the sense of the 19th century (Helmholtz -- Lie -- Klein) it is discussed how the challenges posed by special and general relativity to the classical analysis were taken up by Hermann Weyl and Elie Cartan. Both mathematicians reconsidered the space problem from the point of view of transformations operating in the infinitesimal neighbourhoods of a manifold (spacetime). In a short outlook we survey further developments in mathematics and physics of the second half of the 20th century, in which core ideas of Weyl's and/or Cartan's analysis of the space problem were further investigated (mathematics) or incorporated into basic theories (physics).