Levi-Civita simplifies Einstein. The Ricci rotation coefficients and unified field theories - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Archive for History of Exact Sciences Année : 2023

Levi-Civita simplifies Einstein. The Ricci rotation coefficients and unified field theories

Résumé

This paper concerns late 1920 s attempts to construct unitary theories of gravity and electromagnetism. A first attempt using a non-standard connection—with torsion and zero-curvature—was carried out by Albert Einstein in a number of publications that appeared between 1928 and 1931. In 1929, Tullio Levi-Civita discussed Einstein’s geometric structure and deduced a new system of differential equations in a Rieman- nian manifold endowed with what is nowadays known as Levi-Civita connection. He attained an important result: Maxwell’s electromagnetic equations and the grav- itational equations were obtained exactly, while Einstein had deduced them only as a first order approximation. A main feature of Levi-Civita’s theory is the essential use of the Ricci’s rotation coefficients, introduced by Gregorio Ricci Curbastro many years before. We trace the history of Ricci’s coefficients that are still used today, and highlight their geometric and mechanical meaning.
Fichier non déposé

Dates et versions

hal-04263357 , version 1 (28-10-2023)

Identifiants

Citer

Franco Cardin, Rossana Tazzioli. Levi-Civita simplifies Einstein. The Ricci rotation coefficients and unified field theories. Archive for History of Exact Sciences, 2023, 78 (1), pp.87-126. ⟨10.1007/s00407-023-00322-0⟩. ⟨hal-04263357⟩
22 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More