Feynman, R.P.; The Theory of Positrons
Phys. Rev. 76 (1949) 749;
Reprinted in The Physical Review - the First Hundred Years, AIP Press (1995) CD-ROM.
Selected Papers on Quantum Electrodynamics, editor J. Schwinger, Dover Publications, Inc., New York (1958) 225.
The problem of the behavior of positrons and electrons in given external potentials, neglecting their mutual interaction, is analyzed by replacing the theory of holes by a reinterpretation of the solutions of the Dirac equation. It is possible to write down a complete solution of the problem in terms of boundary conditions on the wave function, and this solution contains automatically all the possibilities of virtual (and real) pair formation and annihilation together with the ordinary scattering
processes, including the correct relative signs of the various terms. In this solution, the "negative energy states'' appear in a form which may be pictured (as by Stückelberg) in space-time as waves traveling away from the external potential backwards in time. Experimentally, such a wave corresponds to a positron approaching the potential and annihilating the electron. A particle moving forward in time (electron) in a potential may be scattered forward in time (ordinary scattering)
or backward (pair annihilation). When moving backward (positron) it may be scattered backward in time (positron scattering) or forward (pair production). For such a particle the amplitude for transition from an initial to a final state is analyzed to any order in the potential by considering it to undergo a sequence of such scatterings. The amplitude for a process involving many such particles is the product of the transition amplitudes for each particle. The exclusion principle requires that
antisymmetric combinations of amplitudes be chosen for those complete processes which differ only by exchange of particles. It seems that a consistent interpretation is only possible if the exclusion principle is adopted. The exclusion principle need not be taken into account in intermediate states. Vacuum problems do not arise for charges which do not interact with one another, but these are analyzed nevertheless in anticipation of application to quantum electrodynamics. The results are
also expressed in momentum-energy variables. Equivalence to the second quantization theory of holes is proved in an appendix.
Related references See also R. P. Feynman, Rev. of Mod. Phys. 20 (1948) 367;
R. P. Feynman, Phys. Rev. 74 (1948) 939;
F. J. Dyson, Phys. Rev. 75 (1949) 486;
G. Wentzel, Einführung in die Quantentheorie der Wellenfelder, Franz Deuticke, Leipzig Chapter V (1943);
W. Pauli, Rev. of Mod. Phys. 13 (1941) 203;
E. C. G. Stückelberg, Helv. Phys. Acta 15 (1942) 23;
W. H. Furry, Phys. Rev. 51 (1937) 125;
W. Pauli, Phys. Rev. 58 (1940) 716;
Creation of the covariant quantum electrodynamic theory. Feynman method.