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The Bootstrap Program for 1+1 Dimensional Field Theoretic Models with Soliton Behaviour

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Field Theoretical Methods in Particle Physics

Part of the book series: NATO Advanced Study Institutes Series ((NSSB,volume 55))

Abstract

A review is given of the present status of the bootstrap program for 1+1 dimensional field theoretic models with soliton behaviour. From the existence of infinitely many conservation laws, unitarity, crossing, “minimality”, internal symmetries, and some assumptions on the one particle spectrum first the exact S-matrix is derived explicitely. We repeat the procedure for the massive Thirring-model (alias Sine-Gordon) S-matrix starting with two fermion (alias soliton) scattering and then deriving the boundstate (alias breather) S-matrix. The same complete S-matrix is obtained by starting with the determination of the boson (breather) S-matrix and then deriving the boson-soliton and soliton-soliton scattering from the assumption that the soliton is a soliton-boson bound state. By means of the same procedure we obtain the Gross-Neveu S-matrix including the kink scattering. Then for some models generalized form factors and Green’s functions for the Z(2)-Ising model in the scaling limit are calculated.

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References

  1. M. Karowski, H. J. Thun, T. T. Truong, P. Weisz, Phys.Lett. 67B, 321 (1977); A. B. and AI. B. Zamolodchikov, Nucl.Phys. B133, 525 (1978); Phys.Lett. 72B, 481 (1978); R. Shankar and E. Witten, Phys.Rev. D17, 2134 (1978); B. Berg and P. Weisz, Nucl.Phys B146, 205 (1978); V. Kurak and J. A. Swieca, Phys.Lett. 82B, 289 (1979); R. Köberle and J. A. Swieca, Factorizable Z(N) Models, S. Carlos preprint (1979).

    ADS  Google Scholar 

  2. M. S. Ablowitz, O. J. Kaup, A. C. Newell, N. Segur, Phys.Rev. Lett. 31, 125 (1973); L. A. Takhtadzhyun and L. D. Faddeev, Theor.Math.Phys. 21, 1046 (1975).

    Article  MathSciNet  ADS  Google Scholar 

  3. R. Dashen, B. Hasslacher and A. Neveu, Phys. Rev. D10, 4114, 4130, 4138, (1974), Dil, 3424 (1975).

    Google Scholar 

  4. S. Coleman, Phys. Rev. D11, 2088 (1975); S. Mandelstam, Phys. Rev. Dil, 3027 (1975); R. Seiler, D. Uhlenbrock, Ann.Phys. 105, 81 (1977); B. Schroer, T. T. Truong, Phys.Rev. D15, 1684 (1977).

    ADS  Google Scholar 

  5. D. Gross and A. Neveu, Phys.Rev. DlO, 3235 (1974).

    ADS  Google Scholar 

  6. R. Shankar and E. Witten, Nucl.Phys. B141, 349 (1978).

    Article  ADS  Google Scholar 

  7. R. Dashen, B. Hasslacher and A. Neveu, Phys.Rev. D12, 2443 (1975).

    MathSciNet  ADS  Google Scholar 

  8. A. B. and AI. B. Zamolodchikov, c. f. ref. [1].

    Google Scholar 

  9. B. Berg and W. Weisz, c. f. ref. [l]; V. Kurak and J. A. Swieca, c. f. ref. [l].

    Google Scholar 

  10. R. Köberle and J. A. Swieca, c. f. ref. [l].

    Google Scholar 

  11. M. D. Kruskal and D. Wiley, American Mathematical Society, Summer Seminar on Nonlinear Wave Motion, ed. A. C. Newell, Potsdam, N.Y. July 1972; B. Berg, M. Karowski and H. J. Thun, Phys.Lett. 62B, 187 (1976), 64B, 286 (1976); B. Yoon, Phys.Rev. D13, 3440 (1976); R. Flume, D. K. Mitter N. Papanicolaou, Phys.Lett. 64B, 289 (1976); P. P. Kulish, E. R. Nissimov, Pisma v JETP 24, 247 (1976).

    Google Scholar 

  12. K. Pohlmeyer, Comm.Math.Phys. 46, 207 (1976); M. Lüscher, K. Pohlmeyer, Nucl.Phys. B137, 48 (1978); H. Eichenherr, M. Forger, preprint Freiburg (Germany) THEP 79/2; E. Brezin C. Itzykson, J. Zinn-Justin, J. B. Zuber, preprint Saclay (France) DPh-T/79/1.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. W. Zimmermann, Ann. Phys. 77, 536 (1973); M. Gomes, J. H. Lowenstein, Phys.Rev. D7, 550 (1973).

    Article  ADS  Google Scholar 

  14. R. Flume, Phys.Lett. 62B, 93 (1976) and corrigendum; B. Berg, M. Karowski, H. J. Thun, Phys.Lett. 62B, 633 (1976); Nuovo Cimento 38A, 11 (1977); R. Flume, S. Meyer, Nuovo Cimento Lett. 18_, 236 (1977); E. R. Nissimov, Bulg. Journ. Phys.L. 113 (1977); J. H. Lowenstein, E. R. Speer, Commun.Math.Phys. 63, 97 (1978); preprint, New York, NYU/TR3/7.

    Google Scholar 

  15. M. Lüscher, Nucl.Phys. B135, 1 (1978).

    Article  ADS  Google Scholar 

  16. P. P. Kulisch, Theor.Math.Phys. 26, 198 (1976); D. Iagolnitzer, Phys. Rev. Dlj3, 1275 (1978).

    Google Scholar 

  17. B. Berg, M. Karowski, W. Theis, H. J. Thun, Phys.Rev. D17, 1172 (1978).

    MathSciNet  ADS  Google Scholar 

  18. B. Berg, M. Karowski, V. Kurak, P. Weisz, Nucl.Phys. B134, 125 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  19. M. Karowski, H. J. Thun, Nucl.Phys. B130, 295 (1977); A. B. Zamolodchikov, Moscow preprint ITEP 12 /1977.

    Google Scholar 

  20. M. Karowski, Nucl.Phys. B153, 244 (1979).

    Article  ADS  Google Scholar 

  21. A. B. Zamolodchikov, Commun.Math.Phys. 55, 183 (1977).

    Google Scholar 

  22. P. Weisz, Nucl.Phys. B122., 1 (1977).

    Google Scholar 

  23. B. Schroer, T. Truong, P. Weisz, Phys.Lett. 63B, 422 (1976).

    Google Scholar 

  24. M. Karowski, H. H. Thun, to be published.

    Google Scholar 

  25. P. Weisz, Phys. Lett. 67B, 179 (1977); A. B. Zamolodchikov, Moscow preprint ITEP 112 (1977).

    Google Scholar 

  26. M. Karowski, P. Weisz, Nucl.Phys. B139, 455 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  27. B. Berg, M. Karowski, P. Weisz, Phys.Rev. D19, 2477 (1979).

    ADS  Google Scholar 

  28. R. Z. Bariev, Phys.Lett. 55A, 456 (1976); B. M. McCoy, C. A. Tracy, T. T. Wu, Phys.Rev.Lett. 3Q, 793 (1977); M. Sato, T. Miwa, M. Jimbo, Proc.Japan Acad. 53A, 6 (1977).

    ADS  Google Scholar 

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Authors and Affiliations

  1. Institut für Theoretische Physik, Freie Universität Berlin, D-1000, Arnimallee 3, Berlin 33, Deutschland

    M. Karowski

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  1. M. Karowski
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Editors and Affiliations

  1. University of Kaiserslautern, Kaiserslautern, Federal Republic of Germany

    Werner Rühl

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© 1980 Plenum Press, New York

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Karowski, M. (1980). The Bootstrap Program for 1+1 Dimensional Field Theoretic Models with Soliton Behaviour. In: Rühl, W. (eds) Field Theoretical Methods in Particle Physics. NATO Advanced Study Institutes Series, vol 55. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3722-5_12

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  • DOI: https://doi.org/10.1007/978-1-4684-3722-5_12

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-3724-9

  • Online ISBN: 978-1-4684-3722-5

  • eBook Packages: Springer Book Archive

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