An Operator Calculus Having Applications in Quantum Electrodynamics

An Operator Calculus Having Applications in Quantum Electrodynamics An alteration in the notation used to indicate the order of operation of noncommuting quantities is sug- gested. Instead of the order being defined by the position on the paper, an ordering subscript is introduced so that A,B^ means AB or BA depending on whether s exceeds s' or vice versa. Then A, 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 functional is discussed in an appendix. Illustrative appli- cations to quantum mechanics are made. In quantum electrodynamics it permits a simple formal under- standing 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 prob- abilities is given.

Authors: Feynman R.P.Pages: 21     Year: 1951

Tags: electrodynamics having applications quantum operator calculus

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