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Lie algebras of local currents and their representations

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Book cover Group Representations in Mathematics and Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 6))

Work supported in part by the National Science Foundation and the U.S. Atomic Energy Commission.

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References

  1. Dashen, R. F., and Sharp, D. H., Phys. Rev., 165, 1857 (1968).

    Google Scholar 

  2. Sharp, D. H., Phys. Rev., 165, 1867 (1968).

    Google Scholar 

  3. Callan, C. G., Dashen, R. F., and Sharp, D. H., Phys. Rev., 165, 1883 (1968).

    Google Scholar 

  4. Sugawara, H., Phys. Rev., 170, 1659 (1968).

    Google Scholar 

  5. The presentation of the material in the first half of this section follows S. L. Adler and R. F. Dashen, Chapter I in Current Algebras, Benjamin, N. Y., (1968). For further background material one can consult other chapters in the Adler-Dashen book as well as B. Renner, Current Algebras and Their Applications, Pergamon, N. Y., (1968), and the lectures of L. Michel and L. O'Raifeartaigh in these Proceedings.

    Google Scholar 

  6. Gell-Mann, M., Phys. Rev., 125, 1067 (1962).

    Google Scholar 

  7. Gell-Mann, M., Physics, 1, 63 (1964.

    Google Scholar 

  8. Adler, S. L., Phys. Rev. Letters, 14, 1051 (1965).

    Google Scholar 

  9. Weisberger, W. I., Phys. Rev. Letters, 14, 1047 (1965).

    Google Scholar 

  10. Todorov, I. T., lectures on quantum field theory. (Not reproduced here)

    Google Scholar 

  11. For reviews of axiomatic field theory see: R. F. Streater and A. S. Wightman, PCT, Spin and Statistics and AN That, Benjamin, N. Y., (1964), and R. Jost, The General Theory of Quantized Fields, American Mathematical Society (1963).

    Google Scholar 

  12. Goldin, G., Ph.D. Thesis, Pinceton University (1968), unpublished.

    Google Scholar 

  13. Goldin, G., “Non-Relativistic Current Algebras as Unitary Representations of Groups”, J. Math. Phys., (to be published).

    Google Scholar 

  14. Grodnik, J., and Sharp, D. H., “Representations of Local Non-Relativistic Currents”Phys. Rev., (to be published).

    Google Scholar 

  15. Grodnik, J., and Sharp, D. H., “Description of Spin and Statistics in NonRelativistic Quantum Theories Based on Local Currents”, Phys. Rev., (to be published).

    Google Scholar 

  16. Grodnik, J., Ph.D. Thesis submitted to the University of Pennsylvania (1969), (unpublished).

    Google Scholar 

  17. Gel'Fand, I., and Vilenkin, N., “Applications of Harmonic Analysis”, Vol. 4 in Genera. Fun., Academic Press, N. Y. (1964).

    Google Scholar 

  18. Mackey, G., Ann. Math., 55, 101 (1952).

    Google Scholar 

  19. Goldin, G., Grodnik, J., Powers, R. T., and Sharp, D. H., “Non-Relativistic Current Algebra in the N/V Limit”, (to be published).

    Google Scholar 

  20. Dicke, A., and Goldin, G., (to be published).

    Google Scholar 

  21. Grodnik, J., and Sharp, D. H., (to be published).

    Google Scholar 

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G. A. Goldin R. Hermann B. Kostant L. Michel C. C. Moore L. O'Raifeartaigh W. Rühl D. H. Sharp I. T. Todorov V. Bargmann

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Goldin, G.A., Sharp, D.H. (1970). Lie algebras of local currents and their representations. In: Goldin, G.A., et al. Group Representations in Mathematics and Physics. Lecture Notes in Physics, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-05310-7_31

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  • DOI: https://doi.org/10.1007/3-540-05310-7_31

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