Abstract
A de Sitter gauge invariant set of field equations is investigated as a possible basis for a gauge description of extended hadrons. The formalism uses an underlying geometric structure given by a fiber bundle over space-time with Cartan connection possessing as fiber a 4-dimensional space of constant curvature characterized by a curvature radius R chosen to be of the order of a Fermi. The constant R represents an elementary length parameter of geometric origin associated with strong interaction physics. A curvature is induced on the bundle space through a hadronic matter distribution described by a generalized bilocal wave field ψ (x, Ξ) where x denotes a point in the base space (space-time) and Ξ varies in the local fiber. An expansion of the internal motion associated with the variable Ξ is given in terms of “de Sitter plane waves”, i.e. the so-called horospherical waves, which are the analogue of the usual plane waves in flat Minkowski space-time. In this context the harmonic analysis of scalar and spinor fields in (4,1) de Sitter space is discussed and its relevance to the SO(4,1) gauge theory is pointed out.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
W. Drechsler, Fortschr.Phys. 23, 607 (1975).
W. Drechsler, Found. of Phys. 7, 629 (1977).
W. Drechsler, Nuovo Cimento, 41A, 597 (1977).
A. Bohm, The Dynamical Group of a Simple Particle Model, in Lectures in Theoretical Physics, Vol. I.XB. Editors: A.0. Barut and W.E. Brittin Gordon and Breach, 1967, p. 327.
A. Bohm, Phys.Rev. 175, 1767 (1968).
A. Bohm, Relativistic Rotators — A Quantum Mechanical de Sitter Bundle, in Proc. of the Int. Symposion on Mathematical Physics, Mexico City 1976, Vol. 2, p. 377.
W. Drechsler, Wave Equation for Extended Hadrons, in Group Theoretical Methods in Physics, Editors. A. Janner, T. Janssen, and M. Boom, Lecture Notes in Physics, Vol. 50, Springer Verlag, 1976, p. 37.
W. Heisenberg, Die Naturwissenschaften 63, 1 (1976).
R. Takahashi, Bull.Soc.Math. France 91, 289 (1963).
W. Drechsler, Phys. Letters, 66B, 439 (1977).
I.M. Gelfand, M.I. Graev, and N.Ya. Vilenkin, Generalized Functions, Vol. 5, Chapter V. Academic Press, London 1966.
E. Schrödinger, Expanding Universe, Cambridge University Press 1956.
Ch. Ehresmann, Colloque de Topologie (espaces fibrés), Bruxelles 1950, p. 29.
W. Drechsler, J.Math.Phys. 18, 1358 (1977).
P.A.M. Dirac, Ann.Math. 36, 657 (1935).
F. Gürsey, and T.D. Lee, Proc.Nat.Acad.Sci. 49, 179 (1963).
W. Drechsler, and R. Sasaki, Nuovo Cimento 46A, 527 (1978).
R. Penrose, Proc.Roy.Soc. (London) 284, 159 (1965).
N.A. Chernikov, and E.A. Tagirov, Ann.Inst. Henri Poincaré 19, 109 (1968).
J.B. Juriyan, N. Mukunda, and E.C.G. Sudarshan, Commun.Math.Phys. 8, 204 (1968).
S. Helgason, Lie Groups and Symmetric Spaces, in Battelle Rencontres, Editors: C.M. De Witt, and J.A. Wheeler, Benjamin Inc. New York 1968, p. 1.
S. Helgason, Functions on Symmetric Spaces, in Homogenous Analysis on Homogenous Spaces. Ann.Math.Soc., Providence, Rhode Island, 1973.
R.S. Strichartz, Journ. of Functional Analysis 12, 341 (1973).
R. Sasaki, Some Classical Solutions of the Sourceless SO(4,1) Gauge Field Equations, Preprint MPI-PAE/PTh 24/78, June 1978.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1979 Springer-Verlag
About this paper
Cite this paper
Drechsler, W. (1979). Geometrically formulated gauge dynamics for extended hadrons. In: Beiglböck, W., Böhm, A., Takasugi, E. (eds) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 94. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09238-2_33
Download citation
DOI: https://doi.org/10.1007/3-540-09238-2_33
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09238-4
Online ISBN: 978-3-540-35345-4
eBook Packages: Springer Book Archive