Advertisement

Il Nuovo Cimento A (1965-1970)

, Volume 51, Issue 2, pp 209–218 | Cite as

Quarks, quaternions and weakly coupled gauge fields

  • B. F. L. Ward
Article

Summary

Using the ring of complex quaternions, the more active view of weakly coupled gauge fields is formulated in such a way that, in theSU2×U1 model of Salam, Ward and Weinberg, for example, ΔS≠0, ΔQ=0 effects are properly suppressed without the appearance of a new quark field in the Lagrangian—only p, n and λ quark fields appear. Here,S is the strangeness andQ is the electric charge. The success of the more active view of theSU2×U1 model in describing\(\Gamma \left( {{\rm K}_L \to \bar \mu \mu } \right)/\left( {\left( {m_{K_L } - m_{Ks} } \right)/m_K } \right)\)% MathType!End!2!1!, charmed particles,\(\psi /J,\psi ',\Upsilon ,\Upsilon '\)% MathType!End!2!1!, etc., in terms of p, n and λ quarks is not disturbed by this new formulation. Here,mK=(mKL+mKs)/2 andma is the mass of a.

Кварки, кватернионы и слабо связанные калибровочные поля

Резюме

Используя кольцо комплексных кватернионов, формулирется подход к слабо связанным калибровочным поям. Причем, в этом подходе в рамках моделиSU2×U2 Салама, Уорда и Вейнберга подавляются, например, эффекты ΔS≠0, ΔQ=0 без появления нового кваркового поля в Лагранжиане —используются только поля р, н и л кварков. ЗдесьS есть странность, аQ—электрический заряд. Предложенный подход в рамках моделиSU2×U1 позволяет успешно описать\(\Gamma \left( {{\rm K}_L \to \bar \mu \mu } \right)/\left( {\left( {m_{K_L } - m_{Ks} } \right)/m_K } \right)\)% MathType!End!2!1!, очарованные частицы,\(\psi /J,\psi ',\Upsilon ,\Upsilon '\)% MathType!End!2!1! и т. д. в терминах р, н и λ кварков. ЗдесьmK=(mKL+mKs)/2 иma есть масса частицы а.

Rissunto

Usando l'anello dei quaternioni complessi, si descrive l'aspetto più attivo dei campi di gauge accoppiati debolmente in maniera tale che nel modelloSU2×U1 di Salam, Ward e Weinberg, per esempio, gli effetti ΔS≠0 e ΔQ=0 siano propriamente soppressi senza la comparsa di un nuovo campo di quark nella lagrangiana—solamente i campi dei quark p, n e λ compaiono.S è la stranezza eQ è la carica elettrica. Il successo dell'aspetto più attivo del modelloSU2×U1 nella descrizione di\(\Gamma \left( {{\rm K}_L \to \bar \mu \mu } \right)/\left( {\left( {m_{K_L } - m_{Ks} } \right)/m_K } \right)\)% MathType!End!2!1!, delle particelle incantate,\(\psi /J,\psi ',\Upsilon ,\Upsilon '\)% MathType!End!2!1! ecc., in termini dei quark p, n e λ non è disturbato da questa nuova formulazione. In questo lavoromK=(mKL+mKs)/2 ema è la massa di a.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    B. F. L. Ward:Nuovo Cimento,48 A 299 (1978).CrossRefADSGoogle Scholar
  2. (2).
    A. Salam andJ. Ward:Nuovo Cimento,11, 568 (1959);S. L. Glashow:Nucl. Phys.,22, 579 (1961);A. Salam andJ. Ward:Phys. Lett.,13, 168 (1964);A. Salam: inElementary Particle Theory, edited byN. Svartholm (New York, N. Y., 1968);S. Weinberg:Phys. Rev. Lett.,19, 1264 (1967).MathSciNetCrossRefGoogle Scholar
  3. (3).
    B. F. L. Ward:Nuovo Cimento,45 A, 523 (1978).CrossRefADSGoogle Scholar
  4. (4).
    B. F. L. Ward:Phys. Rev. Lett.,33, 37, 251 (1974);Phys. Rev. D,16, 2638 (1977);Nuovo Cimento,46 A, 121 (1978).MathSciNetCrossRefADSGoogle Scholar
  5. (5).
    J. J. Aubert, U. Becker, P. J. Biggs, J. Burger, M. Chen, G. Everhart, P. Goldhagen, J. Leong, T. McCorriston, T. G. Rhoades, M. Rhode, S. C. C. Ting, S. L. Wu andY. Y. Wu:Phys. Rev. Lett.,33, 1404 (1974);J.-E. Augustin, A. M. Boyarski, M. Breidenbach, F. Bulos, J. T. Dakin, G. J. Feldman, G. E. Fischer, D. Fryberger, G. Hanson, B. Jean-Marie, R. R. Larsen, V. Lüth, H. L. Lynch, D. Lyon, C. C. Morehouse, J. M. Paterson, M. L. Perl, B. Richter, P. Rapidis, R. F. Schwitters, W. M. Tanenbaum, F. Vanucci, G. S. Abrams, D. Briggs, W. Chinowsky, C. E. Friedberg, G. Goldhaber, R. J. Hollebeek, J. A. Kadyk, B. Lulu, F. Pierre, G. H. Trilling, J. S. Whitaker, J. Wiss andJ. E. Zipse:Phys. Rev. Lett.,33, 1406 (1974).CrossRefADSGoogle Scholar
  6. (6).
    J. D. Bjorken andS. L. Glashow:Phys. Lett.,11, 255 (1964);S. L. Glashow, J. Iliopoulos andL. Maiani:Phys. Rev. D,2, 1285 (1972);G. Goldhaber, F. M. Pierre, G. S. Abrams, M. S. Alam, A. M. Boyarski, M. Breidenbach, W. C. Carithers, W. Chinowsky, S. C. Cooper, R. G. De Voe, J. M. Dorfan, G. J. Feldman, C. E. Friedberg, D. Fryberger, G. Hanson, J. Jaros, A. D. Johnson, J. A. Kadyk, R. R. Larsen, D. Lüke, V. Lüth, H. L. Lynch, R. J. Madaras, C. C. Morehouse, H. K. Nguyen, J. M. Paterson, M. L. Perl, I. Peruzzi, M. Piccolo, T. P. Pun, P. Rapidis, B. Richter, B. Sadoulet, R. H. Schindler, R. F. Schwitters, J. Siegrist, W. Tanenbaum, G. H. Trilling, F. Vannucci, J. S. Whitaker andJ. E. Wiss:Phys. Rev. Lett.,37, 255 (1976);G. Goldhaber: talk given at theConference on the Present Status of Weak-Interaction Physics, Indiana University, May 1977, inA.I.P. Conference Proceedings, No. 37, edited byD. B. Lichtenberg (New York, N. Y., 1977);I. Peruzzi, M. Piccolo, G. J. Feldman, H. K. Nguyen, J. E. Wiss, G. S. Abrams, M. S. Alam, A. M. Boyarski, M. Breidenbach, W. C. Carithers, W. Chinowsky, R. G. De Voe, J. M. Dorfan, G. E. Fischer, C. E. Friedberg, D. Fryberger, G. Goldhaber, G. Hanson, J. A. Jaros, A. D. Johnson, J. A. Kadyk, R. R. Larsen, D. Lüke, V. Lüth, H. L. Lynch, R. J. Madaras, C. C. Morehouse, J. M. Paterson, M. L. Perl, F. M. Pierre, T. P. Pun, P. Rapidis, B. Richter, R. H. Schindler, R. F. Schwitters, J. Siegrist, W. Tanenbaum, G. H. Trilling, F. Vannucci andJ. S. Whitaker:Phys. Rev. Lett.,37, 569 (1976); and references therein.MATHMathSciNetCrossRefADSGoogle Scholar
  7. (7).
    B. F. L. Ward:Nuovo Cimento,44 A, 333 (1978);Lett. Nuovo Cimento,22, 544 (1978).CrossRefADSGoogle Scholar
  8. (8).
    S. W. Herb, D. C. Hom, L. M. Lederman, J. C. Sens, H. D. Snyder, J. K. Yoh, J. A. Appel, B. C. Brown, C. N. Brown, W. R. Innes, K. Ueno, T. Yamanouchi, A. S. Ito, H. Jöstlein, D. M. Kaplan andR. D. Kephart:Phys. Rev. Lett.,39, 252 (1977).CrossRefADSGoogle Scholar
  9. (9).
    See, for example,H. Harari:Theoretical implications of the new particles, inProceedings of the International Symposium on Lepton and Photon Interactions at High-Energies, Stanford, Cal., 1975, edited byW. T. Kirk (Stanford, Cal., 1975).Google Scholar
  10. (10).
    J. D. Edmonds jr.:Inter. Journ. Theor. Phys.,6, 205 (1972);D. Finkelstein, J. M. Jauch, S. Schiminovich andD. Speiser:Journ. Math. Phys.,3, 207 (1962).CrossRefGoogle Scholar
  11. (11).
    J. D. Bjorken andS. D. Drell:Relativistic Quantum Mechanics (New York, N. Y., 1964).Google Scholar
  12. (12).
    See, for example,D. Perkins: Lectures given at the1978 SLAC Summer Institute on Particle Physics, to be published;D. Sheriden: talk presented at the1978 SLAC Topical Conference on Particle Physics, to be published;N. Fortson: talk presented at the1978 SLAC Topical Conference on Particle Physics, to be published;R. M. Barnett: talk presented at the1978 SLAC Topical Conference on Particle Physics, to be published, and references therein.Google Scholar

Copyright information

© Società Italiana di Fisica 1979

Authors and Affiliations

  • B. F. L. Ward
    • 1
    • 2
  1. 1.Stanford Linear Accelerator CenterStanford UniversityStanford
  2. 2.Department of PhysicsPurdue UniversityWest Lafayette

Personalised recommendations