Journal of Mathematical Physics
Feedback | Help | Exit
   
 
 
 
Previous Article
Causal solutions of nonlinear wave and spinor equations obtained by Gel'fand–Shilov regularization
By extending the Gel'fand–Shilov regularization method to products of locally integrable functions it can be shown that the nonlinear Klein–Gordon equations 2u/t2−2u/x21" align="midd...
Next Article
Conservative neutron transport theory
A functional analytic development of the Case full-range and half-range expansions for the neutron transport equation for a conservative medium is presented. A technique suggested by Larsen is used to...

Lie theory and the wave equation in space–time. 3. Semisubgroup coordinates

J. Math. Phys. 18, 271 (1977); doi:10.1063/1.523246

Issue Date: February 1977

You are not logged in to this journal. Log in

E. G. Kalnins
Mathematics Department, University of Waikato, Hamilton, New Zealand

W. Miller, Jr.
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
We classify and study those coordinate systems which permit R separation of variables for the wave equation in four-dimensional space–time and such that at least one of the variables corresponds to a one-parameter symmetry group of the wave equation. We discuss over 100 such systems and relate them to orbits of triplets of commuting operators in the enveloping algebra of the conformal group SO(4,2). Journal of Mathematical Physics is copyrighted by The American Institute of Physics.
Permalink: http://link.aip.org/link/?JMAPAQ/18/271/1
BUY THIS ARTICLE   (US$28)
Download PDF (742 kB) View Cart

PACS

  • 02.20.Sv
    Mathematical methods in physics Group theory Lie algebras of Lie groups
  • 03.40.Kf
    Classical and quantum physics; mechanics and fields Classical mechanics of continuous media: general mathematical aspects Waves and wave propagation: general mathematical aspects
  • YEAR: 1977

PUBLICATION DATA

ISSN:
0022-2488 (print)   1089-7658 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (27)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. L. Gross, J. Math. Phys. 5, 687–95 (1964).
  2. C. Boyer, E. G. Kalnins, and W. Miller, Jr., Nagoya Math. J. 60, 35–80 (1976).
  3. E. G. Kalnins and W. Miller, Jr., J. Math. Phys. 17, 331 (1976).
  4. E. G. Kalnins and W. Miller, Jr., J. Math. Phys. 17, 369 (1976).
  5. E. G. Kalnins, W. Miller, Jr., and P. Winternitz, SIAM J. Appl. Math. 30, 630–64 (1976).
  6. E. G. Kalnins and W. Miller, Jr., J. Math. Phys. 18, 1 (1977).
  7. C. Boyer, E. G. Kalnins, and W. Miller, Jr., J. Math. Phys. 16, 499–511 (1975).
  8. E. G. Kalnins and W. Miller, Jr., J. Math. Phys. 16, 2507–16 (1975).
  9. E. G. Kalnins and W. Miller, Jr., J. Math. Phys. 17, 356 (1976).
  10. G. Post, J. Math. Phys. 17, 24–32 (1976).
  11. H. Bateman, Electrical and Optical Wave-Motion (Dover, New York, 1955), reprint of 1914 ed.
  12. H. Bateman, Partial Differential Equations of Mathematical Physics (Cambridge U.P., Cambridge, 1969), reprint of 1932 ed.
  13. H. Kastrup, Phys. Rev. 140, B183 (1965).
  14. W. Miller, Jr., Symmetry Groups and Their Applications (Academic, New York, 1972).
  15. W. Miller, Jr., Symmetry and Separation of Variables (Addison-Wesley, Reading, Mass., to appear).
  16. P. Dirac, Proc. Cambridge Philos. Soc. 30, 150–63 (1934).
  17. A. Davydov, Quantum Mechanics (Addison-Wesley, Reading, Mass., 1965).
  18. W. Miller, Jr., J. Math. Phys. 13, 1393–99 (1972).
  19. A. Makarov, J. Smorodinsky, K. Valiev, and P. Winternitz, Nuovo Cimento A 52, 1061–84 (1967).
  20. N. Ya. Vilenkin, Special Functions and the Theory of Group Representations (AMS Trans., Am. Math. Soc., Providence, R.I., 1968).
  21. G. Burdet, M. Perrin, and P. Sorba, Commun. Math. Phys. 34, 85–90 (1973).
  22. C. Boyer, Helv. Phys. Acta 47, 589 (1974).
  23. S. Helgason, Differential Geometry and Symmetric Spaces (Academic, New York, 1962).
  24. T. Hirai, Proc. Jpn. Acad. 42, 907–12 (1966).
  25. M. Bôcher, Die Reihentwickelungen der Potentialtheorie (Leipzig, 1894).
  26. L. Eisenhart, Continuous Groups of Transformations (Dover, New York, 1961).
  27. H. Zassenhaus, Can. Math. Bull. 1, 31–39,
    28. 101–11,
    183–91 (1958).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics