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Bound States and Bootstraps in Field Theory

Michael M. Broido*,†

John G. Taylor*

  • Courant Institute of Mathematical Sciences, New York
  • Palmer Physical Laboratory, Princeton University, Princeton, New Jersey

  • Physics Department, Rutgers, The State University, New Brunswick, New Jersey

  • *Partly supported by the National Science Foundation at Rutgers University.
  • †Present address: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York.
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Phys. Rev. 147, 993 – Published 29 July, 1966

DOI: https://doi.org/10.1103/PhysRev.147.993

Abstract

We present a general, model-independent theory of composite particles. Starting from a general local Lagrangian containing an elementary particle, we show how this particle becomes composite (in a precisely defined sense) as its wave-function renormalization constant tends to zero. As this limit is taken, the usual dynamical type of field equation changes its form. We show that the Green's functions of the theory still possess the usual physical interpretation in the limit; in particular, for renormalizable theories, if a certain coupling constant does not tend to zero, the "composite" propagator possesses a pole at the composite mass and with nonzero residue. We show that the operator form of the Green's-function equations describing the composite particle can be manipulated by natural approximations to explain a wide variety of known modeldependent results on composite particles, and in particular to obtain all the usual types of bootstrap equations. We present a preliminary classification of the operator equations, showing that many of them cannot possess physically meaningful solutions. Our results agree qualitatively with earlier, heuristic discussions. Finally we make some remarks about the possibility of "bootstrapped symmetry schemes."

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References (45)

  1. J. G. Taylor, in Proceedings of the Third Eastern U. S. Theoretical Physics Conference, Maryland, 1964 (unpublished) A. Jaffe, E. Nelson, K. Symanzik, J. G. Taylor, and A. Wightman, in The Proceedings of the Cambridge Conference on Mathematical Problems in the Theory of Elementary Particles, 1965 (M.I.T. Press, Cambridge, Massachusetts, to be published)
  2. G. F. Chew, S-M atrix Theory of Strong Interactions (W. A. Benjamin and Company, New York, 1961) M. Jacob and G. F. Chew, Strong Interaction Physics (W. A. Benjamin and Company, New York, 1964)
  3. J. G. Taylor, Nuovo Cimento Suppl. 1, 857 (1963)
  4. J. G. Taylor, Phys. Rev. 136, B1134 (1964)
  5. G. F. Chew and S. C. Frautschi, Phys. Rev. Letters 7, 349 (1961)
  6. E. Abers, F. Zachariasen, and C. Zemach, Phys. Rev. 132, 183 (1963) R. H. Capps, ibid. 132, 2749 (1963) Phys. Rev. Letters 10, 312 (1963) C. de Celles and J. E. Paton, ibid. 11, 251 (1963) L. Cook, C. J. Goebel, and B. Sakita, Argonne report (unpublished) L. Cook and J. E. Paton, Princeton University report (unpublished) R. Cutkosky, Phys. Rev. 131, 1888 (1963) J. S. Dowker and J. E. Paton Nuovo Cimento 30, 450 (1963) J. Fulco and D. Wong, University of California report (unpublished) R. Hwa and H. Patil, Institute for Advanced Study report (unpublished) R. Cutkosky and P. Tarjanne, Phys. Rev. 132, 1355 (1963) R. Dashen and S. Frautschi, ibid. 137, B1331 (1965)
  7. M. Gell-Mann, Phys. Rev. 125, 1067 (1962) Y. Ne'eman, Nucl. Phys. 26, 222 (1961)
  8. D. Lurié and A. Macfarlane, Phys. Rev. 136, B816 (1964) S. Weinberg, Brandeis 1964 Summer Institute Lectures (Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1965), Vol. 2
  9. R. Haag, Phys. Rev. 112, 669 (1958) K. Hepp, Acta Phys. Austriatica 17, 85 (1963) K. Nishijima, Phys. Rev. 111, 995 (1958) D. Ruelle, Helv. Phys. Acta 35, 147 (1962) W. Zimmermann, Nuovo Cimento 10, 597 (1958)
  10. A. Salam, Nuovo Cimento 25, 224 (1962) S. Weinberg, in Proceedings of the 1962 High Energy Physics Conference, (CERN, Geneva, 1962)
  11. A. Wightman, Phys. Rev. 101, 860 (1956) R. Jost, General Theory of Quantized Fields (American Mathematical Society, Providence, Rhode Island, 1965) A. S. Wightman and R. F. Streater, PCT, Spin, Statistics and All That (W. A. Benjamin, Inc., New York, 1964)
  12. R. Peierls, in Proceedings of the Fourth High Energy Physics Conference, Rochester, 1954 (unpublished)
  13. J. Gunson and J. G. Taylor, Phys. Rev. 119, 1121 (1960) J. Gunson, J. Math. Phys. 6, 827, 845, 852 (1965)
  14. J. Gunson and J. G. Taylor, Nuovo Cimento 15, 806 (1960) K. Hepp, Institute for Advanced Study report, 1964 (unpublished)
  15. M. M. Broido (to be published) J. G. Valatin, Proc. Roy. Soc. (London) A226, 254 (1954) K. Wilson, Cornell University report (unpublished)
  16. M. M. Broido, Proc. Cambridge Phil. Soc. 62, 209 (1966) Courant Institute report (unpublished)
  17. J. G. Taylor, in Proceedings of the Siena Conference on Elementary Particles and High Energy Physics, edited by G. Bernandini and G. P. Puppi (Societa Italiana di Fisica, Bologna, 1963)
  18. [3]
  19. I. Bialynicki-Birula, Phys. Rev. 130, 465 (1963)
  20. K. Symanzik, Hercegovni Summer School Proceedings, Jugoslavia, 1961 (unpublished)
  21. [3]
  22. [3], paper VI
  23. P. Kaus and F. Zachariasen, Phys. Rev. 138, B1304 (1965)
  24. N. Bertocchi, Nuovo Cimento 31, 1352 (1964) R. Rockmore, Phys. Rev. 132, 878 (1963) Brookhaven National Laboratory report 8388 (unpublished) S. Weinberg, Phys. Rev. 132, 776 (1963)
  25. I. S. Gerstein, University of Pennsylvania report (unpublished) J.-C. Houard, Ann. Inst. H. Poincaré 2, 105 (1965) J.-C. Houard and B. Jouvet, Nuovo Cimento 18, 446 (1960) M. T. Vaughn, R. Aaron, and R. D. Amado, Phys. Rev. 124, 1258 (1961)
  26. R. Acharya, Nuovo Cimento 24, 870 (1962) J. S. Dowker, ibid. 25, 1135 (1962) ibid.29, 551 (1963) C. R. Hagen, Ann. Phys. (N. Y.) 31, 185 (1965) M. L. Whippman and I. S. Gerstein, Phys. Rev. 134, B1123 (1964)
  27. K. Huang and F. E. Low, J. Math. Phys. 6, 795 (1965) K. Huang and H. Mueller, Phys. Rev. Letters 14, 396 (1965)
  28. W. Guettinger, Nuovo Cimento 36, 968 (1965) B. Lee, K. Mahantappa, I. S. Gerstein, and M. Whippman, Ann. Phys. (N. Y.) 28, 466 (1964) M. Ida, Progr. Theoret. Phys. (Kyoto) 34, 92 (1965)
  29. B. Jouvet, Nuovo Cimento 5, 1 (1957) E. G. P. Rowe, Nucl. Phys. 45, 593 (1963) [8,28]
  30. M. M. Broido, J. Math. Phys. 6, 1702 (1965)
  31. J. G. Taylor, J. Math. Phys. 6, 1148 (1965) ibid.6 (to be published)
  32. S. Weinberg, Phys. Rev. 137, B672 (1965) [M. Ida, Progr. Theoret. Phys. (Kyoto) 35, 104 (1966)]
  33. R. D. Amado, R. Aaron, and Y. Y. Yam, Phys. Rev. Letters 13, 574 (1965)
  34. I. Bialynicki-Birula (private communication)
  35. Pran Nath, University of Pittsburgh report (unpublished) W. J. Abbe, P. Kaus, P. Nath, and Y. N. Srivastava, Phys. Rev. 141, 1513 (1966)
  36. B. Lee and R. F. Sawyer, Phys. Rev. 127, 2266 (1962) J. G. Taylor, paper V [3]
  37. J. G. Taylor, Nuovo Cimento 17, 695 (1960) H. G. Bremerman, Berkeley report (unpublished)
  38. A. S. Wightman, Ann. Inst. Henri Poincaré 1, 403 (1964)
  39. L. Schwartz, Compt. Rend. 239, 847 (1954)
  40. M. M. Broido, Cambridge University report, 1964 (unpublished)
  41. B. L. van der Waerden, Modern Algebra (Frederick Ungar Publishing Company, New York, 1953), especially Chaps. 12-13
  42. M. A. Neumark, Normed Rings (English translation: P. Noordhoff, Ltd., Groningen, The Netherlands, 1959), Sec. 7.5
  43. M. A. Neumark, [42]
  44. M. M. Broido, Churchill dissertation, 1965 (unpublished), especially Chap. 2
  45. M. M. Broido, Courant Institute report (to be published)

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Phys. Rev. 147, 993– Published 29 July, 1966
  • Received 24 June 1965

© 1966 American Physical Society

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