Abstract
Clifford algebra is an ideal medium to express isometry operators. We derive expressions for some members of the holonomy group for n-dimensional spaces with metrics of arbitrary signatures. In particular, we derive expressions for those isometry operators which correspond to coordinate parallelograms that can be continuously shrunk to zero. The isometry operators are expressed in terms of infinite series which are defined by two recursion relations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
W. Ambrose and I. M. Singer, A theorem on holonomy, Trans. Am. Math. Soc. 75 (1953), 428–443.
J. Pérès, Le parallelisms de M. Levi-Civita et la courbure Riemannien, Rendiconti dei Lincei, ser. 5, Vol. 28 (1919), 425–428.
M. Riesz, Clifford Numbers and Spinors, E. Folke Bolinder and Pertti Lounesto, eds., Dordrecht, The Netherlands, Kluwer Academic Publishers, 1993.
J. A. Schouten, Die direkte analysis zur neueren relativitatstheorie, Verhandelingen Kon. Akad. Amsterdam, Vol. 12, No.6 (1918).
J. Snygg, Clifford Algebra — A Computational Tool for Physicists, New York, Oxford University Press, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this chapter
Cite this chapter
Snygg, J. (2000). Specific Representations for Members of the Holonomy Group. In: Ryan, J., Sprößig, W. (eds) Clifford Algebras and their Applications in Mathematical Physics. Progress in Physics, vol 19. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1374-1_9
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1374-1_9
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7119-2
Online ISBN: 978-1-4612-1374-1
eBook Packages: Springer Book Archive