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Lie Algebra as a Unifying Concept in Modern Physics

Published online by Cambridge University Press:  20 November 2018

Edwin Ihrig
Edwin Ihrig*
Affiliation:
Department of Applied Mathematics, McMaster University, Hamilton, Ont. Canada L8S 4K1
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Abstract

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Lie algebras, in the form of algebras of observables, play an essential role in the formulation of classical and quantum mechanics. We discuss whether lie groups play a similar role in general relativity through the holonomy group. We also explore what interrelations these ideas provide between classical physics, relativity and quantum physics.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 4 , 01 December 1977 , pp. 429 - 441
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Abraham, R., (1967), Foundations of Mechanics, Benjamin, New York.Google Scholar
2. Adams, J.F., (1969), Lectures on Lie Groups, Benjamin, New York.Google Scholar
3. Bohr, Å., (1952), The Coupling of Nuclear Surface Oscillations to the Motion of Individual Nucl?ons, K. Danske Vidensk. Selsk, Mat-Fys. Medd. 26 No. 14.Google Scholar
4. Bohr, Å. and Mottelson, B., (1953), Collective and Individual Particle Aspects of Nuclear Structure, K. Danske Vidensk. Selsk, Mat-Fys. Medd. 27 No. 16.Google Scholar
5. Burbidge, G., (1968), The Distribution of Redshifts in Quasi-Stellar Objects, N-systems, and Some Radio and Compact Galaxies Ap J. (letters) 154 L41.Google Scholar
6. Dirac, P. A. M., (1958), The Principles of Quantum Mechanics, Oxford University Press, Oxford.Google Scholar
7. Emch, G., (1972), Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Interscience New York.Google Scholar
8. Hawking, S.W. and Ellis, G. F. R., (1973), The Large Scale Structure of Spacetime, Cambridge University Press, Cambridge.Google Scholar
9. Hicks, N., (1971), Notes on Differential Geometry, Van Nostrand, London.Google Scholar
10. Ihrig, E., (1975), The Uniqueness of gij in Terms of , Int. J. Theor. Phys. 14, p. 23.Google Scholar
11. Ihrig, E., (1976), The Holonomy Group in General Relativity and the Determination of gij from G.R.G. 7, p.313.Google Scholar
12. Ihrig, E., A Local Relativistic Redshift Effect, to appear G.R.G.Google Scholar
13. Ihrig, E., Redshift Formulae for a Local Relativistic Redshift Effect, to appear.Google Scholar
14. Jacobson, N., (1962), Lie Algebras, Interscience, New York.Google Scholar
15. Kobayashi, S. and Nomizu, K., (1963), Foundations of Differential Geometry, Vol. I, interscience, New York.Google Scholar
16. Miller, W., (1972), Symmetry Groups and Their Applications, Academic Press, New York.Google Scholar
17. Misner, C.W.,Thorne, K. S. and Wheeler, J. A., (1970), Gravitation, Freeman and Co. San Francisco.Google Scholar
18. Rosensteel, G., (1975), On the Algebraic Formulation of Collective Models, Ph.D. Thesis, University of Toronto, Toronto, Ontario.Google Scholar
19. Rosensteel, G. and Ihrig, E., Kinetic Energy in the Bohr-Mottelson Collective Model, to appear Phy. Rev.Google Scholar
20. Rosensteel, G. and Rowe, D. J., (1976), The Algebraic CM(3) Model, Annals of Physics 96, p. 1.Google Scholar
21. Rosensteel, G. and Rowe, D. J., (1976), The Sp. (3, R) Model of Nuclear Collective Motion. Invited Talk, 5th International Colloquium on Group Theoretical Methods in Physics, Montreal.Google Scholar
22. Schwarzschild, K., (1916), Uber das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Théorie, Sitzber. Deut. Akad. Wiss. Berlin, Kl. Math-Physics, Tech., p. 189.Google Scholar
23. van Hove, L., (1951), Mem Acad. Roy. Beige., 26.Google Scholar
24. Weyl, H., (1930), Group Theory and Quantum Mechanics, Dover (reprint 1950), New York.Google Scholar