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On the Annihilation of Electrons and Protons

  • P. A. M. Dirac (a1)

An electron, according to relativity quantum theory, has two different kinds of states of motion, those for which the kinetic energy is positive and those for which it is negative. Only the former, of course, can correspond to actual electrons as observed in the laboratory. The latter, however, must also have a physical meaning, since the theory predicts that transitions will take place from one kind to the other. It has recently been proposed that one should assume that nearly all the possible states of negative energy are occupied, with just one electron in each state in accordance with Pauli's exclusion principle, and that the unoccupied states or ‘holes’ in the negative-energy distribution should be regarded as protons. According to these ideas, when an electron of positive energy makes a transition into one of the unoccupied negative-energy states, we have an electron and proton disappearing simultaneously, their energy being emitted in the form of electromagnetic radiation. The object of the present paper is to calculate the frequency of occurrence of these processes of annihilation of electrons and protons.

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* Roy. Soc. Proc. A, vol. 126, p. 360 (1930).

Zeits. f. Phys. vol. 52, p. 853 (1929).

* Strictly one should say the probability of q having a value in the neighbourhood of q′ per unit range of q′.

* Proc. Camb. Philos. Soc. vol. xxv, p. 62 (1929).

* The reduction may conveniently be made with the help of formula (16) in Roy. Soc. Proc. A, vol. CXVII, p. 618 (1928).

* An elementary transition process is one with definite directions of emission and states of polarisation for the emitted photons.

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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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