Lie Algebra as a Unifying Concept in Modern Physics
Canadian mathematical bulletin, Tome 20 (1977) no. 4, pp. 429-441

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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.
Ihrig, Edwin. Lie Algebra as a Unifying Concept in Modern Physics. Canadian mathematical bulletin, Tome 20 (1977) no. 4, pp. 429-441. doi: 10.4153/CMB-1977-063-x
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[1] 1. Abraham, R., (1967), Foundations of Mechanics, Benjamin, New York. Google Scholar

[2] 2. Adams, J.F., (1969), Lectures on Lie Groups, Benjamin, New York. Google Scholar

[3] 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] 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] 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] 6. Dirac, P. A. M., (1958), The Principles of Quantum Mechanics, Oxford University Press, Oxford. Google Scholar

[7] 7. Emch, G., (1972), Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Interscience New York. Google Scholar

[8] 8. Hawking, S.W. and Ellis, G. F. R., (1973), The Large Scale Structure of Spacetime, Cambridge University Press, Cambridge. Google Scholar

[9] 9. Hicks, N., (1971), Notes on Differential Geometry, Van Nostrand, London. Google Scholar

[10] 10. Ihrig, E., (1975), The Uniqueness of g in Terms of , Int. J. Theor. Phys. 14, p. 23. Google Scholar

[11] 11. Ihrig, E., (1976), The Holonomy Group in General Relativity and the Determination of g from G.R.G. 7, p.313. Google Scholar

[12] 12. Ihrig, E., A Local Relativistic Redshift Effect, to appear G.R.G. Google Scholar

[13] 13. Ihrig, E., Redshift Formulae for a Local Relativistic Redshift Effect, to appear. Google Scholar

[14] 14. Jacobson, N., (1962), Lie Algebras, Interscience, New York. Google Scholar

[15] 15. Kobayashi, S. and Nomizu, K., (1963), Foundations of Differential Geometry, Vol. I, interscience, New York. Google Scholar

[16] 16. Miller, W., (1972), Symmetry Groups and Their Applications, Academic Press, New York. Google Scholar

[17] 17. Misner, C.W.,Thorne, K. S. and Wheeler, J. A., (1970), Gravitation, Freeman and Co. San Francisco. Google Scholar

[18] 18. Rosensteel, G., (1975), On the Algebraic Formulation of Collective Models, Ph.D. Thesis, University of Toronto, Toronto, Ontario. Google Scholar

[19] 19. Rosensteel, G. and Ihrig, E., Kinetic Energy in the Bohr-Mottelson Collective Model, to appear Phy. Rev. Google Scholar

[20] 20. Rosensteel, G. and Rowe, D. J., (1976), The Algebraic CM(3) Model, Annals of Physics 96, p. 1. Google Scholar

[21] 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] 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] 23. van Hove, L., (1951), Mem Acad. Roy. Beige., 26. Google Scholar

[24] 24. Weyl, H., (1930), Group Theory and Quantum Mechanics, Dover (reprint 1950), New York. Google Scholar

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