A Generalized Electrodynamics Part II—Quantum

Boris Podolsky and Chihiro Kikuchi
Phys. Rev. 65, 228 – Published 1 April 1944
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Abstract

When the Lagrangian from which the field equations are derived contains second and higher derivatives of the generalized field coordinates, the method of quantizing the field equations developed by Heisenberg and Pauli cannot be immediately applied. By generalizing a method due to Ostrogradsky for converting Lagrange's equations of motion of a particle, when higher derivatives are present, into canonical Hamiltonian form, it becomes possible to perform a similar transformation of the field equations. Applying this method to Podolsky's generalized electrodynamics, we obtain the Hamiltonian of the field and double the usual number of generalized coordinates and momenta. The quantization of the field follows without any special assumptions. The last two sections are devoted to the discussion of the auxiliary conditions and some of their consequences.

  • Received 20 January 1944

DOI:https://doi.org/10.1103/PhysRev.65.228

©1944 American Physical Society

Authors & Affiliations

Boris Podolsky and Chihiro Kikuchi*

  • Department of Physics, University of Cincinnati, Cincinnati, Ohio

  • *Now at Haverford College, Haverford, Pennsylvania.

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Issue

Vol. 65, Iss. 7-8 — April 1944

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