Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-24T22:18:38.908Z Has data issue: false hasContentIssue false
  • English
  • Français

The relativistic quantum mechanics of the elementary particles

Published online by Cambridge University Press:  24 October 2008

H. S. Green
H. S. Green
Affiliation:
Department of Mathematical PhysicsEdinburgh University
Get access Rights & Permissions [Opens in a new window]

Extract

The search for a theory of the elementary particles which is founded on the well-established principles of quantum mechanics and conforms at the same time with the requirements of the principle of relativity has, in recent years, taken several divergent directions. On the one hand, the second quantization of wave fields derived from a Lagrangian by a variational procedure(1) has succeeded in accounting for the existence and most of the properties of the electron, the photon, and the meson. On the other hand, many generalizations of the Dirac wave equation of the electron(2) have been attempted, with applications to the meson(3) and the proton(4). Heisenberg(5) has considered the much more difficult problem of the interaction between different particles, and has found that the key to the situation is the so-called ‘scattering matrix’, which is nothing other than a limiting form of the relativistic density matrix, as defined in § 2 of this paper. It seems probable that the relativistic density matrix ρ; or statistical operator, as it may be called without reference to representation, will play an important part in relativistic quantum mechanics in the future. It satisfies the same equation as the wave function, but differs from it in being a real linear operator, or a dynamical variable, in the terminology of Dirac.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 45 , Issue 2 , April 1949 , pp. 263 - 274
Copyright
Copyright © Cambridge Philosophical Society 1949

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Pauli, W.Rev. Mod. Phys. 13 (1941), 204.CrossRefGoogle Scholar
(2)Dirac, P. A. M.The Principles of Quantum Mechanics (Cambridge, 1947).Google Scholar
(3)Kemmer, N.Proc. Roy. Soc. A, 173 (1939), 91.Google Scholar
(4)Bhabha, H. J.Proc. Indian Acad. Sci. 21 (1945), 241.Google Scholar
(5)Heisenberg, W.Z. Phys. 120 (1943), 513, 673.CrossRefGoogle Scholar
(6)Frenkel, J.J. Phys. 9 (1945), 465.Google Scholar
(7)Klein, O.Ark. Mat. Astr. Fys. 25A, no. 15 (1936).Google Scholar
(8)Dirac, P. A. M.Proc. Roy. Soc. A, 155 (1936), 447.Google Scholar
(9)Fierz, M. and Pauzi, W.Proc. Roy. Soc. A, 173 (1939), 211.Google Scholar
(10)Madhava Rao, B. S.Proc. Indian Acad. Sci. A, 15 (1942), 139.Google Scholar
(11)Madhava Rao, B. S.Proc. Indian Acad. Sci. A, 26 (1947), 221.Google Scholar
(12)Kwal, B. Dissertation (Paris, 1946).Google Scholar
(13)Duffin, R. J.Phys. Rev. 54 (1938), 1114.Google Scholar
(14)Géhéniau, J.L'Electron et Photon (Paris, 1938).Google Scholar
(15)Lubanski, J. K.Physica, 9 (1942), 310.CrossRefGoogle Scholar
(16)Weyl, H.Theory of Groups and Quantum Mechanics (London, 1931).Google Scholar
(17)Heitler, W.Proc. Roy. Irish Acad. 49 (1943), 1.Google Scholar
(18)Lubanski, J. K. and Rosenfeld, L.Physica, 9 (1942), 117.CrossRefGoogle Scholar
(19)Schrödinger, E.Proc. Roy. Irish Acad. 48 (1943), 14.Google Scholar