Abstract
It is shown that it is possible to achieve complete formal symmetrization in the electron and proton quantum theory by means of a new quantization process. The meaning of Dirac equations is somewhat modified and there is no longer any reason to speak of negative-energy states nor to assume, for any other types of particles, especially neutral ones, the existence of antiparticles, corresponding to the “holes” of negative energy.
Translated from Teoria simmetrica dell’elettrone e del positrone, “Il Nuovo Cimento”, vol. 14, 1937, pp. 171–184, by Luciano Maiani. Originally published in, and reprinted with permission from, Soryushiron Kenkyu, vol. 63, issue 3, 1981, pp. 149–162. (Courtesy of L. Maiani). The present translation has been revised by the Editor with the addition of the summary which was missing in “Soryushiron Kenkyu”.
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Notes
- 1.
Dirac, P.A.M.: Proc. Camb. Philos. Soc. 30, 150 (1924). See also Heinsenberg, W.: Z Physik. 90, 209 (1934)
- 2.
Jordan, P., Wigner, E.: Z Physik. 47, 631 (1928)
- 3.
The physical application which will be illustrated later on suggests the more rigorous restriction that, in any linear combination of q r and \(\dot {q}_r\) to any given eigenvalue there corresponds another one, equal in absolute value and opposite in sign.
- 4.
The behaviour of U under space reflection can be conveniently defined taking into account that a simultaneous change of sign of U r has no physical significance, as already implied by other reasons. In our scheme: U′(q) = RU(−q) with R = iρ 1σ y and R 2 = −1. Similarly, for a time reflection: U′(q, t) = iρ 2U(q, −t).
- 5.
Wick, G.: Rend. Accad. Lincei. 21, 170 (1935)
- 6.
Fermi, E.: Rend. Accad. Lincei. 9, 881 (1929)
- 7.
Heisenberg, W., Pauli, W.: Z Physik. 56, 1 (1929); 59, 168 (1930)
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Majorana, E. (2020). A Symmetric Theory of Electrons and Positrons. In: Cifarelli, L. (eds) Scientific Papers of Ettore Majorana. Springer, Cham. https://doi.org/10.1007/978-3-030-23509-3_11
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