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Presymplectic manifolds and the quantization of relativistic particle systems

  • Part II Proceedings Of The Conference Held At Salamanca September 10 – 14, 1979 Edited By P.L. García And A. Pérez-Rendón
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Differential Geometrical Methods in Mathematical Physics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 836))

Abstract

Dynamics of classical and relativistic particle systems is described on the evolution space, which is a presymplectic manifold. Hamiltonian formalism on presymplectic manifolds is investigated and a prequantization procedure for presymplectic manifolds is constructed. A general Pre-Klein-Gordon equation is defined and the prequantization of classical and relativistic particles discussed. The problem of quantizing presymplectic evolution spaces is for (topologically) regular systems reduced to the symplectic case.

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References

  1. Abraham,R./Marsden,J.E.: Foundations of Mechanics (2. ed) [Benjamin/Cummings] Reading, Mass. 1978

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  2. Günther, C.: Prequantum Bundles and Projective Hilbert Geometries Int. Jour. Theor. Phys. 16, 447–464 (1977)

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  3. Kostant, B.: Quantization and Unitary Representations in: Lectures in Modern Analysis and Applications III Taam, C.T. ed., Springer Lecture Notes in Math. 170

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  4. Kostant, B.: Line Bundles and the Prequantized Schrödinger Equation Symp. Math. (1973)

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  5. Sachs, R.K/Wu, H.: General Relativity for Mathematicians [Springer] New York 1977

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  6. Sniatycki, J./Tulczyjew, W.M.: Canocical Relativistic Charged Particles Ann. Inst. H. Poincaré, Sec A, XV, 177–1 (1971)

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  7. Souriau, J.M.: Structure des Systemes Dynamiques [Dunod] Paris 1970

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  8. Sternberg, S./Ungar, Th.: Classical and Prequantized Mechanics without Lagrangians or Hamiltonians (1978)

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Authors and Affiliations

  1. Dept. of Mathematics, TU Berlin, Germany

    C. Günther

Authors
  1. C. Günther
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Editor information

P. L. García A. Pérez-Rendón J. M. Souriau

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© 1980 Springer-Verlag

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Günther, C. (1980). Presymplectic manifolds and the quantization of relativistic particle systems. In: García, P.L., Pérez-Rendón, A., Souriau, J.M. (eds) Differential Geometrical Methods in Mathematical Physics. Lecture Notes in Mathematics, vol 836. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089752

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  • DOI: https://doi.org/10.1007/BFb0089752

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10275-5

  • Online ISBN: 978-3-540-38405-2

  • eBook Packages: Springer Book Archive

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