Abstract
In order to convince you of the relevance of my topic for an Einstein Centennial celebration let me start with a quote.1
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
A. Bohm, Lectures in Theoretical Physics, Boulder Lectures (1966), Vol. 9B, p. 327, Gordon and Breach, A. O. Barut, editor. The idea to picture hadrons as micro-de Sitter spaces of infinite time and finite space extension was suggested in A. O. Barut and A. Bohm, Phys, Rev. 139, B1107 (1965); A. Bohm, Phys. Rev. 145 1212 (1966). The general idea that the “dynamics” of hadrons leads to a “dynamical symmetry group,” which is larger than the space-time symmetry group, has been proposed earlier, see A. O. Barut, Phys. Rev. 135 B839 (1964). de Sitter momentum spaces have been introduced by A. D. Donkov, V. G. Kadyshevsky, M. D. Mateev, and R. M. Mir-Kasimov, Bulgar. Journ. of Physics 1, 58, 150, 233 (1974); 2, 3 (1975); see also V. G. Kadyshevsky, p. 114, in Group Theoretical Methods in Physics, Lecture Notes in Physics, Vol. 94, Springer-Verlag, New York (1979). That this (4+1) de Sitter group be a gauge group of strong interaction was suggested by W. Drechsler using Cartan type fiber bundles in Ref. 2.
W. Drechsler, Fortschritte der Physik 23, 607 (1975).
W. Drechsler, Found. Phys. 7, 629 (1977).
W. Drechsler, “Gauge Theory of Strong and Electromagnetic Interactions Formulated on a Fiber Bundle of Cartan Type,” Texas Lectures, Springer Lecture Notes in Physics, Volume 67 (1977).
E. Cartan, Ann. E. Norm. 40, 325 (1922); 41, 1 (1924); Bull. Sc. Math. 48, 294 (1924). For the general definition of a solder form see S. Kobayashi, Can. J. Math. 8, 145 (1956). For a comparison of Cartan’s viewpoint with the conventional approach to connections, see Comment 5 of S. S.ernberg in Differential Geometrical Methods in Mathematical Physics II, K. Bleuler et al., editors, p. 2, Springer Verlag, 1978.
This is called the unitary gauge choice in K. S. Stelle and P. C. West, Imperical College London preprint ICTP/7879/19.
H. van Dam, L. C. Biedenharn, Phys. Rev. D14, 405 (1976); Physics Letters 62B, 190 (1976).
A. Bohm, Phys. Rev. 175, 1767 (1968). This was based upon an idea by P. Budini and C. Fronsdal, Phys. Rev. Lett. 14, 968 (1965);
V. Ottoson, A. Kihlberg, J. S. Nilsson, Phys. Rev. 137, B658 (1965).
P. A. M. Dirac, J. Math. Phys. 4, 901 (1963).
E. Majorana, Nuovo Cimento 9, 335 (1932).
E. Inönü, E. P. Wigner, Proc. N.A.S. 39, 50 (1953);
A. Bohm, “The Connection Between Representations of SO (4, 1) and the Poincaré Group,” p. 197, Studies in Mathematical Physics, A. O. Barut, ed. (1973);
W. Drechsler, J. Math. Phys. 18, 1358 (1976).
F. Rohrlich, Nucl. Phys. B112, 177 (1978);
L. P. Staunton, Phys. Rev. D13, 3269 (1976);
H. Bacry, J. Math. Phys. 5, 109 (1964);
R. J. Finkelstein, Phys. Rev. 75, 1079 (1949);
H. S. Snyder, Phys. Rev. 71, 38 (1947).
F. Gürsey, Group Theoretical Concepts and Methods in Elementary Particle Physics (1964), p. 365.
C. Fronsdal, Rev. Mod. Phys. 37, 221 (1965).
Gauge groups whose structure constants change over space-time, A. N. Lesnov, V. I. Manko, Lebedev Inst. preprint No. 22, Moscow, 1978 and “bundles” with fibers of different curvatures are generalizations of the conventional differential geometrical concepts whose mathematical foundations have not yet been worked out.
L. Jaffe, J. Math. Phys. 12, 882 (1971).
E. P. Wigner, Unitary Representations of the Inhomogeneous Lorentz Group Including Reflections, Istanbul Lectures (1964). F. Gürsey, ed.
T. E. Kalogeropoulos, G. S. Tzanakos, Proc. of 3rd European Symposium on NN interactions, Stockholm (1976), and private communication;
L. Montanet, Proc. of XIII Rencontres de Moriond, Flaine, France (1978), CERN(EP) Phys. 77–22 (1977);
R. S. Dulude et al., IV International Antiproton Symposium, Strasbourg ( 1978 ), Physics Letters, June 1978;
A. A. Carter et al., Phys. Letters 67B, 117 (1977);
e) A. Apostolakis et al., Phys. Letters 66B, 185 (1977);
f) C. Evangelista et al., Phys. Letters 72B, 139 (1977);
g) A. A. Carter, unpublished, May 1978;
A. Carter, Rutherford Laboratory Preprint RL/78/032 (1978);
R. Baldi et al., Phys. Lett. 74B, 413 (1978).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1980 Plenum Press, New York
About this chapter
Cite this chapter
Bohm, A. (1980). De Sitter Fibers and SO(3,2) Spectrum Generating Group for Hadrons. In: Gruber, B., Millman, R.S. (eds) Symmetries in Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3833-8_6
Download citation
DOI: https://doi.org/10.1007/978-1-4684-3833-8_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-3835-2
Online ISBN: 978-1-4684-3833-8
eBook Packages: Springer Book Archive