L\'eon Rosenfeld's general theory of constrained Hamiltonian dynamics
Abstract
This commentary reflects on the 1930 discoveries of L\'eon Rosenfeld in the domain of phase-space constraints. We start with a short biography of Rosenfeld and his motivation for this article in the context of ideas pursued by W. Pauli, F. Klein, E. Noether. We then comment on Rosenfeld's General Theory dealing with symmetries and constraints, symmetry generators, conservation laws and the construction of a Hamiltonian in the case of phase-space constraints. It is remarkable that he was able to derive expressions for all phase space symmetry generators without making explicit reference to the generator of time evolution. In his Applications, Rosenfeld treated the general relativistic example of Einstein-Maxwell-Dirac theory. We show, that although Rosenfeld refrained from fully applying his general findings to this example, he could have obtained the Hamiltonian. Many of Rosenfeld's discoveries were re-developed or re-discovered by others two decades later, yet as we show there remain additional firsts that are still not recognized in the community.
Keywords
Cite
@article{arxiv.1606.06076,
title = {L\'eon Rosenfeld's general theory of constrained Hamiltonian dynamics},
author = {Donald Salisbury and Kurt Sundermeyer},
journal= {arXiv preprint arXiv:1606.06076},
year = {2017}
}
Comments
61 pages. Commentary on Rosenfeld's "Zur Quantelung der Wellenfelder", Ann. Phys. 5, 113 (1930). A translation into English by us will appear in European Physical Journal H. This commentary will also appear in EPJH. Revision contains more elementary examples, an appendix with an overview of constrained Hamiltonian dynamics, additional references, and corrections of typos