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Variations on (X,ψ) Duality

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Book cover Direct and Inverse Problems of Mathematical Physics

Part of the book series: International Society for Analysis, Applications and Computation ((ISAA,volume 5))

Abstract

We sketch some possible extensions of the (X, ψ) duality ideas of Faraggi-Matone [15, 16] in two directions. First one looks at a formulation in terms of Baker-Akhiezer (BA) functions of integrable systems and secondly we sketch some of the Olavo theory of [25] in order to indicate possible connections.

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References

  1. Bonelli, G. and M. Matone, (1996). Phys. Rev. Lett., Vol. 76, (pages 41074110 ).

    Google Scholar 

  2. Carroll, R. (1997). hep-th 9705229, Nucl. Phys. B, Vol. 502, to appear.

    Google Scholar 

  3. Carroll, R. hep-th 9607219, 9610216, and 9702138.

    Google Scholar 

  4. Carroll, R. and Y. Kodama, (1995). Jour. Phys. A, Vol. 28, (pages 63736387).

    Google Scholar 

  5. Carroll, R. (1994). Jour. Nonlin. Sci., Vol. 4, (pages 519–544); Teor. Mat. Fizika, Vol. 99, (1994), (pages 220–225 ).

    Google Scholar 

  6. Carroll, R. (1995). Proc. NEEDS’94, World Scientific, (pages 24–33 ).

    Google Scholar 

  7. Carroll, R. (1993/1995). Applicable Anal., Vol. 49, (1993), (pages 1–31); Vol. 56, (1995), (pages 147–164 ).

    MATH  Google Scholar 

  8. Carroll, R. (1991). Topics in soliton theory, North-Holland.

    Google Scholar 

  9. Carroll, R. and J.H. Chang, (1997). Applicable Anal., Vol. 64, (pages 343378 ).

    Google Scholar 

  10. Carroll, R. (1996). Repts. Math. Phys., Vol. 37, (pages 1–21 ).

    Article  MATH  Google Scholar 

  11. Carroll, R. Proc. Conf. Supersymmetry and integrable models, UIC, June, 1997, Springer, to appear.

    Google Scholar 

  12. Carroll, R. In preparation.

    Google Scholar 

  13. Chang, J.H. Thesis, Univ. of Illinois, In preparation.

    Google Scholar 

  14. Cohen, L. (1966). Jour. Math. Phys., Vol. 7, (pages 781–786 ).

    Article  Google Scholar 

  15. Faraggi, A. and M. Matone, (1997). Phys. Rev. Lett., Vol. 78, (pages 163166 ).

    Google Scholar 

  16. Faraggi, A. and M. Matone. hep-th 9705108.

    Google Scholar 

  17. Floyd, E. quant-ph 9707051.

    Google Scholar 

  18. Guha, P. and K. Takasaki, solv-int 9705013.

    Google Scholar 

  19. Holland, P. (1993). The quantum theory of motion, Cambridge Univ. Press.

    Google Scholar 

  20. Kodama, Y. and J. Gibbons, (1990). Workshop on nonlinear and turbulent processes in physics, World Scientific, (pages 166–180 ).

    Google Scholar 

  21. Matsukidaira, J., J. Satsuma, and W. Strampp, (1990). Jour. Math. PHys., Vol. 31, (pages 1426–1434 ).

    Article  MathSciNet  MATH  Google Scholar 

  22. Messiah, A. (1995). Quantum mechanics, Vol. 1, North-Holland.

    Google Scholar 

  23. Nakatsu, T. and K. Takasaki, (1996). Mod. Phys. Lett. A, Vol. 11, (pages 157–168 ).

    MathSciNet  MATH  Google Scholar 

  24. Ohta, Y., J. Satsuma, D. Takahashi, and T. Tokihiro, (1988). Prog. Theor. Phys., Supp. 94, (pages 210–244 ).

    Article  MathSciNet  Google Scholar 

  25. Olavo, L. quant-ph 9503020,9503021,9503022,9503024,9503025,9509012, 9509013, 9511028, 9511039, 9601002, 9607002, 9607003, 9609003, 9609023, 9703006, 9704004.

    Google Scholar 

  26. Reif, F. (1965). Fundamentals of statistical and thermal physics, McGraw-Hill.

    Google Scholar 

  27. Seiberg, N. and E. Witten, (1994). Nucl. Phys. B, Vol. 426, (pages 19–52); Vol. 431, (pages 484–550 ).

    Article  MathSciNet  MATH  Google Scholar 

  28. Takasaki, K. and T. Takebe, (1992/1995). Inter. Jour. Mod. Phys. A, Supp. 1992, (pages 889–922); Rev. Math. Phys., Vol. 7, (1995), (pages 743–808 ).

    MathSciNet  MATH  Google Scholar 

  29. Tegmark, M. quant-ph 9709032.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Mathematics Department, University of Illinois, Urbana, IL, 61801, USA

    Robert Carroll

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  1. Robert Carroll
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Editor information

Editors and Affiliations

  1. University of Delaware, USA

    Robert P. Gilbert

  2. Kyushu University, Japan

    Joji Kajiwara

  3. University of Tennessee at Chattanooga, USA

    Yongzhi S. Xu

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Carroll, R. (2000). Variations on (X,ψ) Duality. In: Gilbert, R.P., Kajiwara, J., Xu, Y.S. (eds) Direct and Inverse Problems of Mathematical Physics. International Society for Analysis, Applications and Computation, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3214-6_3

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  • DOI: https://doi.org/10.1007/978-1-4757-3214-6_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4818-2

  • Online ISBN: 978-1-4757-3214-6

  • eBook Packages: Springer Book Archive

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