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Hamiltonian Systems with Spin

Published online by Cambridge University Press:  20 November 2018

J. E. Marsden
J. E. Marsden*
Affiliation:
Princeton University.
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In this note we give a brief exposition of the mathematical foundations of the theory of spin for both classical and quantum mechanical systems on oriented Riemannian manifolds. We shall use freely the notations and theory developed in Abraham [1] and Marsden [2, 3], From the physical point of view nothing new appears. The whole purpose of the note is to explain how the theory fits in the spirit of [1].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 2 , April 1969 , pp. 203 - 208
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Abraham, R. and Marsden, J., Foundations of mechanics. (Benjamin, N.Y., 1967).Google Scholar
2. Marsden, J., Generalized Hamiltonian mechanics. Arch. for Rat. Mech. and Analysis 28, 5 (1968) 323–361 Google Scholar
3. Marsden, J., Hamiltonian one-parameter groups. Arch. for Rat. Mech. and Analysis 28, 5 (1968) 362–396.Google Scholar
4. Palais, R., Seminar on the Atiyah Singer Index Theorem. Annals of Math. Studies (Princeton, 1963).Google Scholar
5. Milnor, J., Spin structures on manifolds. l'ensign. math. (1963).Google Scholar
6. Milnor, J., Representation rings of some classical groups. Mimeographed. (Princeton University).Google Scholar
7. Cartan, E., Theory of spinors. (MIT Press, 1966).Google Scholar
8. Lang, S., Algebra. (Addison Wesley, 1965).Google Scholar
9. Greenberg, M., Lectures on algebraic topology. (Benjamin, N. Y., 1966).Google Scholar
10. Bacry, H., Classical Hamiltonian formalism for spin. (Argonne National Laboratory, Argonne, 111.).Google Scholar
11. Dankel, T., Thesis. (Princeton, 1968).Google Scholar
12. Marsden, J. and Abraham, R., Hamiltonian systems on Lie groups and hydrodynamics. Proc. Inst. of Global Analysis (Berkeley, 1969).Google Scholar