Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Conformal transformations and Clifford algebras

Authors: Pertti Lounesto and Esko Latvamaa
Journal: Proc. Amer. Math. Soc. 79 (1980), 533-538
MSC: Primary 15A66; Secondary 81C40
MathSciNet review: 572296
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A spinor representation for the conformal group of the real orthogonal space $ {R^{p,q}}$ is given. First, the real orthogonal space $ {R^{p,q}}$ is compactified by adjoining a (closed) isotropic cone at infinity. Then the nonlinear conformal transformations are linearized by regarding the conformal group as a factor group of a larger orthogonal group. Finally, the spin covering group of this larger orthogonal group is realized in the Clifford algebra $ {R_{1 + p,q}}$ containing the Clifford algebra $ {R_{p,q}}$ on the orthogonal space $ {R^{p,q}}$. Explicit formulas for orthogonal transformations, translations, dilatations and special conformal transformations are given in Clifford language.

References [Enhancements On Off] (What's this?)

  • [1] M. F. Atiyah, R. Bott, and A. Shapiro, Clifford modules, Topology 3 (1964), no. suppl. 1, 3–38. MR 0167985
  • [2] Claude C. Chevalley, The algebraic theory of spinors, Columbia University Press, New York, 1954. MR 0060497
  • [3] J. Haantjes, Conformal representations of an n-dimensional euclidean space with a non-definite fundamental form on itself, Nederl. Akad. Wetensch. Proc. 40 (1937), 700-705.
  • [4] Max Karoubi, 𝐾-theory, Springer-Verlag, Berlin-New York, 1978. An introduction; Grundlehren der Mathematischen Wissenschaften, Band 226. MR 0488029
  • [5] H. A. Kastrup, Zur Physikalischen Deutung und darstellungsthoretischen Analyse der konformen Transformationen von Raum und Zeit, Ann. Physik (7) 9 (1961/1962), 388–428 (German). MR 0144690
  • [6] -, Some experimental consequences of conformal invariance at extremely high energies, Phys. Letters 3 (1962), 78-80.
  • [7] Ian R. Porteous, Topological geometry, Van Nostrand Reinhold Co., London-New York-Melbourne, 1969. MR 0254852
  • [8] Irving Ezra Segal, Mathematical cosmology and extragalactic astronomy, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Pure and Applied Mathematics, Vol. 68. MR 0496337

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 15A66, 81C40

Retrieve articles in all journals with MSC: 15A66, 81C40

Additional Information

Article copyright: © Copyright 1980 American Mathematical Society