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Dynamical Problems of the Relativistic Quark Model

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Recent Developments in Mathematical Physics

Part of the book series: Acta Physica Austriaca ((FEWBODY,volume 11/1973))

Abstract

In our lectures we deal with the specific dynamical problems arising in the formulation of the relativistic quark model in the framework of field theory1. After the discussion of some basic questions occurring in this particular attempt towards a foundation of hadron dynamics, we develop extensively the methods for the description of mesons as quark-antiquark bound-states and give some illuminating phenomenological applications. In order to outline the spirit of our approach, let us first answer some general questions.

Lectures given at XII. Internationale Universitätswochen für Kernphysik, Schladming, February 5 – 17, 1973.

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References

  1. Chapter A is partly based on Lectures by H. Joos, Quark Theory of Elementary Particles, Instituto de Fisica Teorica, Sao Paulo (1969).

    Google Scholar 

  2. Textbooks on general Quantum Field Theory, for example, L. Klein (Editor), “Dispersion Relations and the Abstract Approach to Field Theory” ( New York, Gordon and Breach Publishers Inc. 1961 ).

    Google Scholar 

  3. R. Jost, “The General Theory of Quantized Fields”, Providence: American Mathematical Soc. (1965).

    MATH  Google Scholar 

  4. R. Jost (Editor), Teoria quantistica locale, New York and London, Academic Press (1969).

    Google Scholar 

  5. R. Haag, Phys. Rev. 112, (1958) 669.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. W. Zimmermann, Nuovo Cim. X, (1958) 597.

    Article  Google Scholar 

  7. D. Ruelle, Hely. Phys. Acta 35 (1962) 147.

    MATH  MathSciNet  Google Scholar 

  8. W. Zimmermann, Nuovo Cim. 13 (1959) 503

    Article  MATH  Google Scholar 

  9. W. Zimmermann, ibid. 16 (1960) 690.

    MATH  Google Scholar 

  10. For a review on this work see: R. Haag, Brandeis Lectures 1970.

    Google Scholar 

  11. W. Thirring, Nuclear Phys. 10, 97 (1959).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. S. Sakata, Progr. Theor. Phys. 16, 686 (1956).

    Article  ADS  Google Scholar 

  13. J. Wess, Nuovo Cim. 15, 52 (1960).

    Article  MathSciNet  Google Scholar 

  14. M. Gell-Mann, Physics Lett. 8, 214 (1964).

    Article  ADS  Google Scholar 

  15. G. Zweig, CERN preprints TH 401, 412 (1964) (unpublished).

    Google Scholar 

  16. H. J. Lipkin, Proc. of the Lund Int. Conf. on Elementary Particles, p. 51 (Lund 1969 ).

    Google Scholar 

  17. G. Preparata, Massive Quarks and Deep Inelastic Phenomena, Universita di Roma (Preprint).

    Google Scholar 

  18. O. W. Greenberg, Phys. Rev. Lett. 13, 598 (1964).

    Article  ADS  Google Scholar 

  19. T. Goto, O. Hara, and S. Ishida, Progr. Theor. Phys. 43, 849 (1970).

    Article  ADS  Google Scholar 

  20. J. G. Körner, Nuclear Phys. B25, 282 (1970).

    Google Scholar 

  21. M. Y. Han and Y. Nambu, Phys. Rev. 139B, 1006 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  22. M. Gell-Mann, in “Elementary Particle Physics”, p.733 (P. Urban ed., Springer, Wien-New York, 1972 ).

    Google Scholar 

  23. We thank Prof. K. Symanzik for a hint in this direction.

    Google Scholar 

  24. Dynamics based on generalized Veneziano formulas seem to correspond to infinite component fields. For ref. see: V. Alessandrini, D. Amati, M. Le Bellac, D. Olive, Phys. Rep. lc, No. 6 (1971).

    Google Scholar 

  25. R. J. Rivers, Nuovo Cim. 11A, 178 (1972).

    Article  ADS  Google Scholar 

  26. For dynamical quark n-point functions based on the Veneziano formula see: M. Bando, S. Machida, H. Nakkagawe, and K. Yamawaki, Progr. Theor. Phys. 47, 626 (1972) and literature quoted there.

    Article  ADS  Google Scholar 

  27. On a more kinematical level, phenomenological questions in the framework of QUARFT were discussed by: T. Gudehus, DESY 68/11.

    Google Scholar 

  28. C. H. Llewellyn-Smith, Ann. Phys. (N.Y.) 53, 521 (1969).

    Article  Google Scholar 

  29. M. Gell-Mann, Physica 1, 63 (1964).

    Google Scholar 

  30. J. V. Allaby et al., Nuovo Cim. 64A, 75 (1969).

    Article  ADS  Google Scholar 

  31. Yu. M. Antipov et al., Physics Lett. 29B, 245 (1969).

    Article  ADS  Google Scholar 

  32. M. Bott-Bodenhausen et al., Physics Lett. 40B, 693 (1972).

    ADS  Google Scholar 

  33. R. Hagedorn, Nuovo Cim. Suppl. 6, 311 (1968).

    Google Scholar 

  34. V. M. Maksimenko et al., Sov. Phys. - JETP Lett. 3, 214 (1966).

    ADS  Google Scholar 

  35. T. Massam, The Quark Hunters’ Progress, CERN 68–24.

    Google Scholar 

  36. T. Massam, The Quark Hunters’ Progress, CERN 68–24. Y. S. Kim, N. Kwak, Fields and Quanta 3, 1 (1972).

    Google Scholar 

  37. J. J. de Swart, Phys. Rev. Lett. 18, 618 (1967).

    Article  ADS  Google Scholar 

  38. F. Low, Comments Nucl. and Part. Phys. 1, 52, 85 (1967).

    MathSciNet  Google Scholar 

  39. H. Fritzsch, M. Gell-Mann, Proc. of the XVI Int. Conference on High Energy Physics, Chicago-Batavia, Vol. 2, 135 (1972).

    Google Scholar 

  40. K. Johnson, Phys. Rev. D6, 1101 (1972).

    ADS  Google Scholar 

  41. Similar ideas were proposed by: H. Suura, Physics Lett. 42B, 237 (1972).

    Google Scholar 

  42. Heavy quarks were introduced in a non-relativistic framework by: G. Morpurgo, Physics 2, 95 (1965).

    Google Scholar 

  43. G. Källen, Helv. Phys. Acta, 25, 417 (1952).

    MATH  Google Scholar 

  44. H. Lehmann, Nuovo Cim. 11, 342 (1954).

    Article  MATH  MathSciNet  Google Scholar 

  45. S. S. Schweber, Relativistic Quantum Field Theory, p. 659 ( Harper and Row, New York 1961 ).

    Google Scholar 

  46. We thank G. Preparata for a clarifying discussion on this point.

    Google Scholar 

  47. We omit technical details. In view of the fact, that all hadrons may be generated by a+e annihilation, this assumption might be even justified in physics. Compare also: R. F. Dashen, D.H. Sharp, Phys. Rev. 165, 1857 (1968).

    Article  ADS  Google Scholar 

  48. J. M. G. Fell, Transact. Am. Math. Soc. 94, 365 (1960).

    MATH  MathSciNet  Google Scholar 

  49. R. Haag, D. Kastler, Journ. Math. Phys. 5, 848 (1964).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  50. S. Doplicher, R. Haag, J. E. Roberts, Commun. Math. Phys. 23, 199 (1971).

    Article  ADS  MathSciNet  Google Scholar 

  51. K. Symanzik, Journ. Math. Phys. 1, 249 (1960).

    Article  ADS  MathSciNet  Google Scholar 

  52. for references see: K. Symanzik, “Many-Particle Structure of Green’s Functions”, Symposia on Theoretical Physics, Vol.3, 121 (1967), (Plenum Press, 1967 ).

    Google Scholar 

  53. J. G. Taylor, Phys. Rev. 150, 1321 (1966).

    Article  ADS  Google Scholar 

  54. D. Z. Freedman, C. Lovelace and J. M. Namyslowski, Nuovo Cim. 43A, 258 (1966).

    Article  ADS  Google Scholar 

  55. This form is due to K. Symanzik (unpublished).

    Google Scholar 

  56. H. A. Bethe, E. E. Salpeter, Phys. Rev. 84, 1232 (1951).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  57. M. Gell-Mann, F. Low, Phys. Rev. 84, 350 (1951).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  58. S. Mandelstam, Proc. Roy. Soc. A233, 248 (1955).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  59. R. E. Cutkosky, M. Leon, Phys. Rev. 135B, 1445 (1964).

    Article  ADS  MathSciNet  Google Scholar 

  60. R. Meyer, Dissertation, Hamburg (1972); internal report DESY-T-72/10.

    Google Scholar 

  61. R. Dolen, D. Horn, and C. Schmid, Phys. Rev. Lett. 19, 402 (1967)

    Article  ADS  Google Scholar 

  62. R. Dolen, D. Horn, and C. Schmid, Phys. Rev. 166, 1772 (1968).

    ADS  Google Scholar 

  63. Application to meson-meson scattering: C. Lovelace, Physics Lett. 28B, 264 (1968).

    ADS  Google Scholar 

  64. E. D. Bloom, F. J. Gilman, Phys. Rev. Lett. 25, 1140 (1970)

    Article  ADS  Google Scholar 

  65. E. D. Bloom, F. J. Gilman, Phys. Rev. D4, 2901 (1971).

    ADS  Google Scholar 

  66. M. Böhm, H. Joos, M. Krammer, DESY 72 /62 (1972).

    Google Scholar 

  67. A. Bramon, E. Etim, M. Greco, Physics Lett. 41B, 609 (1972).

    Google Scholar 

  68. A. Salam, R. Delbourgo, J. Strathdee, Proc. Roy. Soc. (London) A284, 146 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  69. T. Gudehus, DESY-Report 68 /11 (1968).

    Google Scholar 

  70. M. Böhm, T. Gudehus, Nuovo Cim. 57A, 578 (1968).

    Article  ADS  Google Scholar 

  71. H. Suura, B.-L. Young, Nuovo Cim. 11A, 101 (1972).

    Article  ADS  Google Scholar 

  72. see f.i.: G. Morpurgo in “Theory and Phenomenology in Particle Physics” part A, p. 84 (Editor A. Zichichi, Academic Press New York, London (1969)).

    Google Scholar 

  73. J. J. J. Kokkedee, “The Quark Model” (W. A. Benjamin, Inc. New York (1969)).

    Google Scholar 

  74. H. Harari, Phys. Rev. Lett. 22, 562 (1969).

    Article  ADS  Google Scholar 

  75. J. Rosner, Phys. Rev. Lett. 22, 689 (1969).

    Article  ADS  Google Scholar 

  76. Y. Takahashi, Nuovo Cim. 6, 370 (1957).

    Google Scholar 

  77. F. Gutbrod told us about the importance of considering modifications of S’(q) according to (3.14) in phenomenological bound state models of e.m. interactions. (Compare F. Gutbrod, DESY 72 /74 (1972).

    Google Scholar 

  78. M. Gell-Mann, Ref. 14, for the relation between constituent quarks and current quarks.

    Google Scholar 

  79. J. J. J. Kokkedee, l.c.; O.W. Greenberg, Proc. of the Lund Int. Conf. on Elementary Particles, p. 385 (Lund 1969 ).

    Google Scholar 

  80. R. H. Dalitz, “Symmetries and the Strong Interactions”, Proc. of the XIIIth International Conference on High Energy Physics, Berkeley (1966) 215.

    Google Scholar 

  81. R. H. Dalitz, “Mesonic Resonance States”, Meson Spectroscopy, p. 497 (C. Baltay, A. H. Rosenfeld ed., New York (1968)).

    Google Scholar 

  82. Ref. 34. An extensive review of the theory of the B S equation has been given by: N. N. kanishi, Progr. Theor. Phys. Suppl. 43, 1 (1969).

    Article  ADS  Google Scholar 

  83. M. Böhm, H. Joos, M. Krammer, Nuovo Cim. 7A, 21 (1972)

    Article  ADS  Google Scholar 

  84. M. Böhm, H. Joos, M. Krammer, “Concepts in Hadron Physics”, p. 407 (Springer-Verlag, Wien, New York, 1971 ).

    Google Scholar 

  85. M. K. Sundaresan, P. J. S. Watson, Ann. Phys. (N.Y.) 59, 375 (1970).

    Article  ADS  MathSciNet  Google Scholar 

  86. G. Preparata, in “Subnuclear Phenomena”, p. 240 (1969 International School of Physics E. Majorana, Erice).

    Google Scholar 

  87. G. C. Wick, Phys. Rev. 96, 1124 (1954).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  88. M. Gourdin, Nuovo Cim. 7, 338 (1958).

    Article  MATH  Google Scholar 

  89. A. Erdelyi, ed., “Higher Transcendental Functions”, Vol. 2 ( McGraw-Hill, New York, 1953 ).

    Google Scholar 

  90. E. Zur Linden, H. Mitter, Nuovo Cim. 61B, 389 (1969).

    Article  ADS  Google Scholar 

  91. A. Pagnamenta, Nuovo Cim. 53A, 30 (1968).

    Article  ADS  Google Scholar 

  92. See Ref. 51 and P. Becher, Diplomarbeit, Würzburg (1972).

    Google Scholar 

  93. M. Ciafaloni, P. Menotti, Phys. Rev. 1408, 929 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  94. R. P. Feynman, M. Kislinger, F. Ravndal, Phys. Rev. D3, 2706 (1971).

    Article  ADS  Google Scholar 

  95. M. Böhm, H. Joos, M. Krammer, Nuclear Phys. B51, 397 (1973).

    Article  ADS  Google Scholar 

  96. M. K. Sundaresan and P. J. S. Watson, Ref. 51.

    Google Scholar 

  97. B. L. v. d. Waerden, “Die gruppentheoretische Methode in der Quantenmechanik”, p. 78… (Springer, Berlin 1932 ).

    Google Scholar 

  98. See f.i.: A. R. Edmonds, “Angular Momentum in Quantum Mechanics” (Princeton Univ. Press, 1957 ).

    Google Scholar 

  99. S. Mandelstam, Proc. Roy. Soc. A237, 496 (1956).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  100. H. M. Lipinski, D. R. Snider, Phys. Rev. 176, 2055 (1968).

    Article  ADS  Google Scholar 

  101. R. F. Keam, Journ. Math. Phys. 9, 1462 (1968).

    Google Scholar 

  102. R. F. Keam, ibid. 10, 594 (1969).

    Google Scholar 

  103. R. F. Keam, ibid. 11, 394 (1970).

    Google Scholar 

  104. R. F. Keam, ibid. 12, 515 (1971).

    MathSciNet  Google Scholar 

  105. R. Delbourgo, A. Salam, J. Strathdee, Nuovo Cim. 50A, 193 (1967).

    Article  Google Scholar 

  106. P. Breitenlohner, MPI-Preprint (1970).

    Google Scholar 

  107. P. Narayanaswamy, A. Pagnamenta, Nuovo Cim, 53A, 635 (1968).

    Article  ADS  Google Scholar 

  108. K. Ladânyi, Preprint, Tübingen (1972).

    Google Scholar 

  109. J. S. Goldstein, Phys. Rev. 91, 1516 (1953).

    Article  MATH  ADS  Google Scholar 

  110. S. N. Biswas, H. S. Green, Nuclear Phys. 2, 177 (1956)

    Article  MATH  ADS  Google Scholar 

  111. A. Bastai, L. Bertocchi, G. Furlan, M. Tonin, Nuovo Cim. 30, 1532 (1963).

    Article  MATH  MathSciNet  Google Scholar 

  112. W. Kummer, Nuovo Cim. 31, 219 (1964);

    Article  MathSciNet  Google Scholar 

  113. W. Kummer, ibid. 34, 1840 (1964).

    Google Scholar 

  114. K. Seto, Progr. Theor. Phys. 42, 1394 (1969).

    Google Scholar 

  115. H. Ito, Progr. Theor. Phys. 43, 1035 (1970).

    Article  MATH  ADS  Google Scholar 

  116. N. Nakanishi, Journ. Math. Phys. 12, 1578 (1971).

    MATH  Google Scholar 

  117. D. Zum Winkel, Diplomarbeit, Hamburg (in preparation).

    Google Scholar 

  118. H. Harari, Proc. of the 14th International Conference on High-Energy Physics, Vienna (1968), p. 195.

    Google Scholar 

  119. H. J. Lipkin, Ref. 10.

    Google Scholar 

  120. W. Thirring, in “Subnuclear Phenomena” (1.c.) p.200.

    Google Scholar 

  121. M. Krammer, internal report DESY-T 73/1.

    Google Scholar 

  122. H. Joos, Fortschritte der Physik 10, 65 (1962).

    Article  MATH  Google Scholar 

  123. Review of particle properties, Particle Data Group, Physics Lett. 39B, 1 (1972).

    Article  Google Scholar 

  124. M. Böhm, H. Joos, M. Krammer, DESY 72 /62 (1972).

    Google Scholar 

  125. T. Kobayashi, Progr. Theor. Phys. 48, 335 (1972).

    Article  ADS  Google Scholar 

  126. H. Pietschmann, W. Thirring, University of Vienna, Scientific Note No. 32 (1965).

    Google Scholar 

  127. R. van Royen, V. F. Weisskopf, Nuovo Cim. 50, 617 (1967);

    Article  ADS  Google Scholar 

  128. R. van Royen, V. F. Weisskopf, ibid. 51, 583 (1967).

    ADS  Google Scholar 

  129. J. Lefrancois, Proc. of the 1971 Int. Symposium on Electron and Photon Interactions at High Energies, p. 51 (Cornell Univ.).

    Google Scholar 

  130. G. Barbarino et al., Lett. Nuovo Cim. 3, 689 (1972).

    Article  Google Scholar 

  131. G. Smadja et al., in “Experimental Meson Spectroscopy 1972” (Third Philadelphia Conference) p. 349.

    Google Scholar 

  132. F. Ceradini et al., Physics Lett. 43B, 341 (1973).

    Article  ADS  Google Scholar 

  133. J. J. Sakurai, D. Schildknecht, Physics Lett. 40B, 121 (1972).

    ADS  Google Scholar 

  134. N. Cabibbo, R. Gatto, Phys. Rev. 124, 1577 (1961).

    Article  ADS  Google Scholar 

  135. R. P. Feynman, Proc. of the Third Topical Conference on High Energy Collisions of Hadrons, Stony Brook. ( Gordon and Breach, New York, 1969 ).

    Google Scholar 

  136. H. Fritzsch, M. Gell-Mann, Proc. of the Coral Gables Conference on Fundamental Interactions at High Energy, Vol. 2, p. 1 ( Gordon and Breach, New York, London, Paris, 1971 ).

    Google Scholar 

  137. S. Weinberg, Phys. Rev. Lett. 18, 507 (1967).

    Article  ADS  Google Scholar 

  138. Electromagnetic meson decays in the P+V-S model were discussed recently by D. Flamm and J. Sanchez; Lett. Nuovo Cim. 6, 129 (1973).

    Article  Google Scholar 

  139. R. Delbourgo, M. A. Rashid, A. Salam, J. Strathdee, Proc. of the Seminar on High Energy Physics and Elementary Particles (Trieste 1965 ) p. 455.

    Google Scholar 

  140. For a review on relativistic generalizations of SU(6) we refer to: H. Ruegg, W. Rühl, T.S. Santhanam, H.lv. Phys. Acta 40, 9 (1967).

    Google Scholar 

  141. L. I. Schiff, Phys. Rev. Lett. 17, 612 (1966).

    Article  ADS  Google Scholar 

  142. O. W. Greenberg, Phys. Rev. 150, 1177 (1966).

    Article  ADS  Google Scholar 

  143. G. Morpurgo, Physics Lett. 20, 684 (1966).

    Article  ADS  Google Scholar 

  144. G. Morpurgo, Ref. 42. H. J. Lipkin, Phys. Rev. 159, 1303 (1967).

    Article  Google Scholar 

  145. Such modified couplings are suggested by experiment: M. Afzal et al., Nuovo Cim. 15A, 61 (1973).

    Article  ADS  Google Scholar 

  146. J. Nuttal, Phys. Rev. 160, 1459 (1967).

    Article  ADS  Google Scholar 

  147. D. B. Lichtenberg, Phys. Rev. 178, 2197 (1969).

    Article  ADS  Google Scholar 

  148. A. N. Mitra, Nuovo Cim. 56A, 1164 (1968).

    Article  ADS  Google Scholar 

  149. For a review of three-particle scattering we refer to: W. Sandhas, in “Elementary Particle Physics” (l.c.) p. 57.

    Google Scholar 

  150. J. G. Taylor, Ref. 32.

    Google Scholar 

  151. O. W. Greenberg, Ref. 12.

    Google Scholar 

  152. G. Berendt, E. Weimar, private communication.

    Google Scholar 

  153. G. Berendt, E. Weimar, Lett. Nuovo Cim. 5, 613 (1972).

    Article  Google Scholar 

  154. L. Susskind, Phys. Rev. Lett. 23, 545 (1969).

    Article  ADS  Google Scholar 

  155. D. Geffen (private communication).

    Google Scholar 

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Authors and Affiliations

  1. Physikalisches Institut, Universität Würzburg, Germany

    M. Böhm

  2. Deutsches Elektronen-Synchrotron, DESY, Hamburg, Germany

    H. Joos & M. Krammer

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  1. M. Böhm
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  2. H. Joos
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  3. M. Krammer
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Editors and Affiliations

  1. Universität Graz, Graz, Australia

    Paul Urban (Vorstand des Institutes für Theoretische Physik) (Vorstand des Institutes für Theoretische Physik)

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Böhm, M., Joos, H., Krammer, M. (1973). Dynamical Problems of the Relativistic Quark Model. In: Urban, P. (eds) Recent Developments in Mathematical Physics. Acta Physica Austriaca, vol 11/1973. Springer, Vienna. https://doi.org/10.1007/978-3-7091-7654-2_2

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