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An operator calculus having applications in quantum electrodynamics

Feynman, Richard P. (1951) An operator calculus having applications in quantum electrodynamics. Physical Review, 84 (1). pp. 108-128. ISSN 0031-899X.

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An alteration in the notation used to indicate the order of operation of noncommuting quantities is suggested. Instead of the order being defined by the position on the paper, an ordering subscript is introduced so that AsBs′ means AB or BA depending on whether s exceeds s′ or vice versa. Then As can be handled as though it were an ordinary numerical function of s. An increase in ease of manipulating some operator expressions results. Connection to the theory of functionals is discussed in an appendix. Illustrative applications to quantum mechanics are made. In quantum electrodynamics it permits a simple formal understanding of the interrelation of the various present day theoretical formulations. The operator expression of the Dirac equation is related to the author's previous description of positrons. An attempt is made to interpret the operator ordering parameter in this case as a fifth coordinate variable in an extended Dirac equation. Fock's parametrization, discussed in an appendix, seems to be easier to interpret. In the last section a summary of the numerical constants appearing in formulas for transition probabilities is given.

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Additional Information:©1951 The American Physical Society. Received 23 May 1951. The author has profited from discussions with M. Peshkin and L. Brown.
Issue or Number:1
Record Number:CaltechAUTHORS:FEYpr51
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3530
Deposited By: Tony Diaz
Deposited On:12 Jun 2006
Last Modified:02 Oct 2019 23:04

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