The European Physical Journal H

, Volume 42, Issue 1, pp 23–61

Léon Rosenfeld’s general theory of constrained Hamiltonian dynamics

Open Access

DOI: 10.1140/epjh/e2016-70042-7

Cite this article as:
Salisbury, D. & Sundermeyer, K. EPJ H (2017) 42: 23. doi:10.1140/epjh/e2016-70042-7


This commentary reflects on the 1930 general theory of Léon Rosenfeld dealing with 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.

Copyright information

© The Author(s) 2017

Open access funding provided by Max Planck Society.

Open Access This is an open access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Max Planck Institute for the History of ScienceBerlinGermany
  2. 2.Austin CollegeShermanUSA
  3. 3.Freie Universität Berlin, Fachbereich PhysikBerlinGermany

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