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Discussion of the infinite distribution of electrons in the theory of the positron

  • P. A. M. Dirac (a1)

The quantum theory of the electron allows states of negative kinetic energy as well as the usual states of positive kinetic energy and also allows transitions from one kind of state to the other. Now particles in states of negative kinetic energy are never observed in practice. We can get over this discrepancy between theory and observation by assuming that, in the world as we know it, nearly all the states of negative kinetic energy are occupied, with one electron in each state in accordance with Pauli's exclusion principle, and that the distribution of negative-energy electrons is unobservable to us on account of its uniformity. Any unoccupied negative-energy states would be observable to us, as holes in the distribution of negative-energy electrons, but these holes would appear as particles with positive kinetic energy and thus not as things foreign to all our experience. It seems reasonable and in agreement with all the facts known at present to identify these holes with the recently discovered positrons and thus to obtain a theory of the positron.

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* As this theory was first put forward, Proc. Roy. Soc. A, 126, p. 360 (1930) and Proc. Camb. Phil. Soc. 26, p. 361 (1930), the holes were assumed to be protons, but this assumption was afterwards seen to be untenable, since it was found that the holes must correspond to particles with the same rest-mass as electrons. See Proc. Roy. Soc. A, 133, p. 61 (1931).

* Dirac, , Proc. Camb. Phil. Soc. 25, p. 62 (1929); 26, p. 376 (1930) and 27, p. 240 (1931).

* The word ‘all’ used in this connection means each of a set of orthogonal states which is made as large as possible, and does not include states formed by superposition of these orthogonal states.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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