Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-13T17:20:31.883Z Has data issue: false hasContentIssue false
  • English
  • Français

VII.—On the Geometry of Dirac's Equations and their Expression in Tensor Form

Published online by Cambridge University Press:  15 September 2014

H. S. Ruse
H. S. Ruse
Affiliation:
University College, Southampton
Get access

Extract

The purpose of the present paper is to give as simple an account as possible of the general-relativity theory of two-component spinors, and to investigate its geometrical and analytical consequences. The work was suggested by courses of lectures given at Edinburgh in 1932 and 1935 by Professor E. T. Whittaker, who, on the basis of the special-relativity spinor theory of van der Waerden (1929), obtained the completely tensorized form of Dirac's equations given by him in a recent paper (1937).

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 57 , 1938 , pp. 97 - 127
Copyright
Copyright © Royal Society of Edinburgh 1938

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 to Literature

Baker, H. F., 1923. Principles of Geometry (Cambridge), vol. iii, chap. i.Google Scholar
De Broglie, L., 1934. L'électron magnétique (Paris).Google Scholar
Darwin, C. G., 1928 a. “Wave Equations of the Electron,” Proc. Roy. Soc. (A), vol. cxviii, pp. 654–680.Google Scholar
Darwin, C. G., 1928 b. “On the Magnetic Moment of the Electron,” Proc. Roy. Soc. (A), vol. cxx, pp. 621–631.Google Scholar
Eisenhart, L. P., 1926. Riemannian Geometry (Princeton), chap. iii.Google Scholar
Infeld, L., and van der Waerden, B. L., 1933. “Die Wellengleichung des Elektrons in der Allgemeinen Relativitätstheorie,” S.B. Preuss. Akad. Wiss., pp. 380–401.Google Scholar
Lamson, K. W., 1930. “Some Differential and Algebraic Consequences of the Einstein Field Equations,” Trans. Amer. Math. Soc., vol. xxxii, pp. 709–722.CrossRefGoogle Scholar
Laporte, O., and Uhlenbeck, G. E., 1931 a. “Application of Spinor Analysis to the Maxwell and Dirac Equations,” Phys. Rev., vol. xxxvii, pp. 1380–1397.CrossRefGoogle Scholar
Laporte, O., and Uhlenbeck, G. E., 1931 b. “New Covariant Relations following from the Dirac Equations,” Phys. Rev., vol. xxxvii, pp. 1552–1554.Google Scholar
von Laue, M., 1933. “Korpuskular- und Wellentheorie,” Handbuch der Radiologie (Marx), vol. vi, pt. i, pp. 1–114, and in particular § 8, pp. 89–102.Google Scholar
Ruse, H. S., 1936. “On the Geometry of the Electromagnetic Field in General Relativity,” Proc. London Math. Soc., vol. xli, pp. 302–322.CrossRefGoogle Scholar
Schouten, J. A., 1931. “Dirac Equations in General Relativity (Four-dimensional Theory),” Journ. Math. Phys. Mass. Inst. Tech., vol. x, pp. 239–271.Google Scholar
Schouten, J. A., 1933. “Zur generellen Feldtheorie: Semivektoren und Spinraum,” Zeits. Phys., vol. lxxxiv, pp. 92–111.CrossRefGoogle Scholar
Sommerville, D. M. Y., 1934. Analytical Geometry of Three Dimensions (Cambridge), chap. xvi.Google Scholar
Struik, D. J., 1927–28. “On Sets of Principal Directions in a Riemannian Manifold of Four Dimensions,” Journ. Math. Phys. Mass. Inst. Tech., vol. vii, pp. 193–197.Google Scholar
Veblen, O., 1933. “Geometry of Two-component Spinors,” Proc. Nat. Acad. Sci. Washington, vol. xix, pp. 462–474.CrossRefGoogle Scholar
Veblen, O., and Whitehead, J. H. C., 1932. Foundations of Differential Geometry (Cambridge Tract No. 29), chap. v.Google Scholar
van der Waerden, B. L., 1929. “Spinoranalyse,” Gött. Nach., pp. 100–109.Google Scholar
Weyl, H., 1931. The Theory of Groups and Quantum Mechanics (Methuen, London).Google Scholar
Whittaker, E. T., 1938. “On the Relations of the Tensor-calculus to the Spinorcalculus,” Proc. Roy. Soc. (A), vol. clviii, pp. 38–46.Google Scholar