dorsal/arxiv
View SchemaLocal spinor structures in V. Fock's and H. Weyl's work on the Dirac equation (1929)
| Authors | Erhard Scholz |
|---|---|
| Categories | |
| ArXiv ID | physics/0409158 |
| URL | https://arxiv.org/abs/physics/0409158 |
Abstract
In early 1929, V. Fock (initially in collaboration with D. Iwanenko) and H. Weyl developed independently from each other a general relativistic generalization of the Dirac equation. In the core, they arrived at the same theory by the introduction of a local (topologically trivial) spinor structures and a lifting of the Levi-Civita connection of underlying space-time. They both observed, in slightly different settings, a characteristic underdetermination of the spin connection by a complex phase factor, which gave the symbolical possibility for a reformulation of Weyl's old (1918) idea to characterize the electromagnetic potential by a differential form transforming as a gauge field. Weyl and Fock realized the common mathematical core of their respective approaches in summer 1929, but insisted on differences in perspective. An interesting difference was discussed by Weyl in his Rouse Ball lecture in 1930,. He contrasted the new type of unification strongly to the earlier geometrically unified field theories (including his own). He was quite explicit that he now considered his earlier ideas on geometrization of ``all of physics'' as premature and declared that the new, more empirically based approach would have to go a long way before it could be considered as a true "geometrization" of matter structures.
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"abstract": "In early 1929, V. Fock (initially in collaboration with D. Iwanenko) and H.\nWeyl developed independently from each other a general relativistic\ngeneralization of the Dirac equation. In the core, they arrived at the same\ntheory by the introduction of a local (topologically trivial) spinor structures\nand a lifting of the Levi-Civita connection of underlying space-time. They both\nobserved, in slightly different settings, a characteristic underdetermination\nof the spin connection by a complex phase factor, which gave the symbolical\npossibility for a reformulation of Weyl\u0027s old (1918) idea to characterize the\nelectromagnetic potential by a differential form transforming as a gauge field.\nWeyl and Fock realized the common mathematical core of their respective\napproaches in summer 1929, but insisted on differences in perspective. An\ninteresting difference was discussed by Weyl in his Rouse Ball lecture in\n1930,. He contrasted the new type of unification strongly to the earlier\ngeometrically unified field theories (including his own). He was quite explicit\nthat he now considered his earlier ideas on geometrization of ``all of\nphysics\u0027\u0027 as premature and declared that the new, more empirically based\napproach would have to go a long way before it could be considered as a true\n\"geometrization\" of matter structures.",
"arxiv_id": "physics/0409158",
"authors": [
"Erhard Scholz"
],
"categories": [
"physics.hist-ph"
],
"title": "Local spinor structures in V. Fock\u0027s and H. Weyl\u0027s work on the Dirac equation (1929)",
"url": "https://arxiv.org/abs/physics/0409158"
},
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