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Mathematical formulation of the quantum theory of electromagnetic interaction

Feynman, R. P. (1950) Mathematical formulation of the quantum theory of electromagnetic interaction. Physical Review, 80 (3). pp. 440-457. ISSN 0031-899X. doi:10.1103/PhysRev.80.440.

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The validity of the rules given in previous papers for the solution of problems in quantum electrodynamics is established. Starting with Fermi's formulation of the field as a set of harmonic oscillators, the effect of the oscillators is integrated out in the Lagrangian form of quantum mechanics. There results an expression for the effect of all virtual photons valid to all orders in e2/hc. It is shown that evaluation of this expression as a power series in e2/hc gives just the terms expected by the aforementioned rules. In addition, a relation is established between the amplitude for a given process in an arbitrary unquantized potential and in a quantum electrodynamical field. This relation permits a simple general statement of the laws of quantum electrodynamics. A description, in Lagrangian quantum-mechanical form, of particles satisfying the Klein-Gordon equation is given in an Appendix. It involves the use of an extra parameter analogous to proper time to describe the trajectory of the particle in four dimensions. A second Appendix discusses, in the special case of photons, the problem of finding what real processes are implied by the formula for virtual processes. Problems of the divergences of electrodynamics are not discussed.

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Additional Information:©1950 The American Physical Society. Received 8 June 1950. The author appreciates his opportunities to discuss these matters with Professor H. A. Bethe and Professor J. Ashkin, and the help of Mr. M. Baranger with the manuscript.
Issue or Number:3
Record Number:CaltechAUTHORS:FEYpr50
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3528
Deposited By: Tony Diaz
Deposited On:12 Jun 2006
Last Modified:08 Nov 2021 19:56

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