Léon Rosenfeld's general theory of constrained Hamiltonian dynamics

Abstract

This commentary reflects on the 1930 discoveries of Léon 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.

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

References in corpus (2)

• Covariantized Noether identities and conservation laws for perturbations in metric theories of gravity
• Local spinor structures in V. Fock's and H. Weyl's work on the Dirac equation (1929)

Cited by in corpus (13)

• Construction of quantum Dirac observables and the emergence of WKB time
• A Lagrangian constraint analysis of first order classical field theories with an application to gravity
• Superintegrable relativistic systems in spacetime-dependent background fields
• Equivalent Theories Redefine Hamiltonian Observables to Exhibit Change in General Relativity
• Covariant canonical formulations of classical field theories
• On the canonical formulation of gauge field theories and Poincare transformations
• Singular Lagrangians and the Dirac--Bergmann Algorithm in Classical Mechanics
• Relaxation of first-class constraints and the quantization of gauge theories: from "matter without matter" to the reappearance of time in quantum gravity
• What Are Observables in Hamiltonian Einstein-Maxwell Theory?
• A road map for Feynman's adventures in the land of gravitation
• Does a Second-Class Primary Constraint Generate a Gauge Transformation? Electromagnetisms and Gravities, Massless and Massive
• Tales from the prehistory of Quantum Gravity. Léon Rosenfeld's earliest contribution
• Observables and Hamilton-Jacobi approaches to general relativity. I. The Earlier History