Il Nuovo Cimento A (1971-1996)

, Volume 96, Issue 1, pp 1–51 | Cite as

On the detectability of the dirac string

  • M. H. Saffouri


Theoretical arguments are adduced to point out difficulties with the concept of an isolated magnetic monopole introduced by Dirac. In particular, it is shown by explicit calculations that the Dirac string must interact with charged particles. It will always scatter electrons. The introduction of aLS coupling will also lead to the existence of two bound states for electrons in a uniform magnetic field whether confined or not. It is then demonstrated that Dirac’s theory is actually a theory of the electromagnetic string rather than a theory of the monopole. The connection between the Dirac theory and the Bohm-Aharonov effect is also investigated. The Dirac-Yang principle, which underlies Dirac’s considerations, is introduced and discussed.


12.40 Models of strong intreactions 

О детектируемости ди раковских струи


Приводятся теоретич еские аргументы, указывающие на трудн ости концепции изолированного магн итного монополя, введ енного Дираком. В частности, показывается, что стр уна Дирака должна взаимодействовать с заряженными частица ми. Эта струна всегда при водит к рассеянию эле ктронов. Введение LS-связи будет также приводит ь к существованию дву х связанных состояний электроно в, движущихся в одородн ом магнитном поле, кот орое может быть ограниченным или неограниченным. З атем показывается, чт о теоря Дирака в действитель ности является теорией эле ктромагнитной струн ы, а не теорией монополя. Так же исследуется связь между теорией Д ирака и эффектом Ааро нова-Бома. Вводится и обсуждает ся принцип Дирака-Янга, к оторый лежит в основе рассмотрения Дирака.


Si presentano degli argomenti teorioi per mettere in evidenza difficoltà inerenti il concetto di monopolo isolate introdotto da Dirac. In particolare, si dimostra, tramite calcolo esplicito, ehe la stringa di Dirac dovrebbe interagire con le particelle eariche. Queste saranno sempre soggette ad un effetto di diffusione. In aggiunta, l’introduzione di un accoppiamento di tipoLS porterà all’esistenza di due stati legati per gli elettroni ehe si muovono in un campo magnetico uniforme che può essere conflnato o meno. In conseguenza si dimostra che la teoria di Dirac è piuttosto una teoria della stringa elettromagnetica che non una teoria di monopolo. La relazione tra la teoria di Dirac e l’effetto Bohm-Aharonov è anche preso in considerazione. II prinoipio di Dirac-Yang, che sta alla base delle considerazioni di Dirac, è introdotto e discusso.


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  1. (1).
    H. Weyl:Z. Phys.,56, 330 (1929).ADSCrossRefGoogle Scholar
  2. (2).
    P. A.M. Dirac:Proc. R. Soc. London, Ser. A,133, 60 (1931).ADSCrossRefGoogle Scholar
  3. (3).
    M. H. Saffouri:Nuovo Cimento D,3, 589 (1984);J. Phys. A,16, 4377 (1983).ADSMathSciNetCrossRefGoogle Scholar
  4. (4).
    J. D. Jackson:Classical Electrodynamics, 2nd Edition (John Wiley and Sons Inc., New York, N. Y., 1975). On p. 219 Jackson writes: « But it is often convenient to introduce potentials, obtaining a smaller number of second-order equations, while satisfying some of the Maxwell equations identically ».zbMATHGoogle Scholar
  5. (5).
    M. Jammer:Concepts of Force (Harvard University Press, Cambridge, Mass., 1957), Chapt. 11.Google Scholar
  6. (6).
    H. Heetz:The Principles of Mechanics Presented in a New Form, (Dover, New York, N. Y., 1956).Google Scholar
  7. (7).
    Thus on p. 156 of Ms celebrated article on quantum mechanics in theHandbuch der Physik, Vol.1 (Springer-Verlag, Berlin, 1958), Pauli could still say that « only the field strengths have a direct physical significance ».Google Scholar
  8. (8).
    C. N. Yang andE. L. Mills Phys. Rev.,96, 191 (1954).ADSCrossRefGoogle Scholar
  9. (9).
    C. Quigg:Gauge Theories of the Strong, the Weak, and Electromagnetic Interactions (The Benjamin Cummings Publ. Co., Menlo Park, Cal, 1983).zbMATHGoogle Scholar
  10. (10).
    J. D. Jackson which we cite in ref. (4) above.Google Scholar
  11. (11).
    B. S. Deaver jr. andW. M. Faibbank:Phys. Rev. Lett.,7, 43 (1961);R. Doll andM. Nabauer:Phys. Rev. Lett.,7, 51 (1961).ADSCrossRefGoogle Scholar
  12. (12).
    N. Byers andC. N. Yang:Phys. Rev. Lett.,7, 46 (1961).ADSCrossRefGoogle Scholar
  13. (13).
    L. Onsager:Phys. Rev. Lett.,7, 50 (1961).ADSCrossRefGoogle Scholar
  14. (14).
    G. Wentzel:Prog. Theor. Phys. Suppl,37-38, 163 (1966).ADSCrossRefGoogle Scholar
  15. (15).
    M. Fierz:helv. Phys. Acta,37, 663 (1964).MathSciNetGoogle Scholar
  16. (16).
    A. O. Barut andG. L. Baruzin:Nucl. Phys. B,81, 477 (1974).ADSCrossRefGoogle Scholar
  17. (17).
    A. O. Bakut:J. Phys. A,11, 2073 (1978).ADSCrossRefGoogle Scholar
  18. (18).
    D. Zwanziger:Phys. Rev. B,137, 647 (1965).ADSMathSciNetCrossRefGoogle Scholar
  19. (19).
    E. Recami andR. Mignani:A new theoretical and experimental outlook on magnetic monopoles, inThe Uncertainty Principle and Foundations of Quantum Mechanics, edited by W. R. Price and S. S. Chissick (John Wiley and Sons, London, 1977), p. 321.Google Scholar
  20. (20).
    A. Salam:Phys. Lett.,22, 683 (1966).ADSCrossRefGoogle Scholar
  21. (21).
    J. G. Taylor:Phys. Rev. Lett.,18, 713 (1967).ADSCrossRefGoogle Scholar
  22. (22).
    L. Landau:Nucl. Phys.,3, 127 (1957).CrossRefGoogle Scholar
  23. (23).
    P.A. M. Dirac:Phys. Rev.,74, 817 (1948).ADSCrossRefGoogle Scholar
  24. (24).
    B. Zumino:recent developments in the theory of magnetically charged particles, inStrong and Weak Interactions: Present Problems, edited by A. Zichichi (Academic Press, New York, N. Y., 1966), p. 711.CrossRefGoogle Scholar
  25. (25).
    A. Tonomura, N. Osakabe, T. Matsuda, T. Kawasaki, J. Endo, S. Yano andH. Yamada:Phys. Rev. Lett.,56, 792 (1986).ADSCrossRefGoogle Scholar
  26. (26).
    L. Page:Phys. Rev.,36, 444 (1930).ADSCrossRefGoogle Scholar
  27. (27).
    E. U. Condon andG. H. Shoetley:The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1963), Chapt. V.Google Scholar
  28. (28).
    E. Jahnke, F. Emde andF. Lösch:Tables of Higher Functions (McGraw-Hill, Book Co., Inc., New York, N. Y., 1960), Chapts. IV, VIII, IX.zbMATHGoogle Scholar
  29. (29).
    N. W. McLachlan:Bessel Functions for Engineers, 2nd Edition (Clarendon Press, Oxford, 1955).zbMATHGoogle Scholar
  30. (30).
    L. Schiff:Quantum Mechanics, 2nd Edition (McGraw-Hill Book Co., Inc., New York, N. Y., 1955), Chapt. V.zbMATHGoogle Scholar
  31. (31).
    C. N. Yang:Gauge fields, electromagnetism and the Bohm-Aharonov effect, inProceedings of the International Symposium, on Foundations of Quantum Mechanics, edited by S. Kamefuchi (Physical Society of Japan, Tokyo, 1983), p. 5.Google Scholar
  32. (32).
    Y. Aharonov andD. Bohm:Phys. Rev.,115, 485 (1959).ADSMathSciNetCrossRefGoogle Scholar
  33. (34).
    H. Poincarè:Compt. Rend.,123, 530 (1896). One of the latest and most significant is the following:S. D. Drell, N.M. Korll, M. T. Mueller, S. J. Parke andM. A. Ruderman:Phys. Rev. Lett., 50, 644 (1983).Google Scholar
  34. (35).
    Wu and Yang:T. T. Wu andC. N. Yang:Phys. Rev. D,12, 3845 (1975).ADSMathSciNetGoogle Scholar
  35. (36).
    p.87 in ref. (7).Google Scholar
  36. (37).
    J. Slàdkovà:Interference of Light (IIiffe Books Ltd., 1968, London), Chapt. 3.Google Scholar
  37. (38).
    W. Ehrenberg andR. E. Siday:Proc. Phys. Soc. London, Sect. B,62, 8 (1949).ADSCrossRefGoogle Scholar
  38. (39).
    C. N. Yang:Ann. N. Y. Acad. Sci.,294, 68 (1977).)CrossRefGoogle Scholar
  39. (40).
    N. S. Craigie, P. Goddard andW. Nahm, Editors:Proceedings of the Monopole Meeting, I.O.T.P., December 1981 (World Scientific Publ. Co., Singapore, 1982), p. (iii).Google Scholar
  40. (41).
    G. Giacomelli:Conference highlights and summation Experimental, inMonopole ’83, edited by J. L. Stone (Plenum Press, New York, N. Y., 1984), p. 637.CrossRefGoogle Scholar
  41. (43).
    E. Katz:Am. J. Phys.,33, 306 (1965).ADSCrossRefGoogle Scholar
  42. (44).
    L. D. Landau andE. Y. Lifshitz:Quantum Mechanics, 3rd Edition (Pergamon Press, Oxford, 1977), Chapt. XV.zbMATHGoogle Scholar
  43. (16).
    A. Erdèlyi, Editor:Higher Transcendental Functions (McGraw-Hill Book Co Inc, New York, N. Y., 1953),Vol. 2.zbMATHGoogle Scholar
  44. (46).
    I. S. Gradshteyn andI. M. Ryzik:Table of Integrals, Series and Products (Academic Press, New York, N. Y., 1980), pp. (xxxiv), 123.Google Scholar
  45. (47).
    V. Mangulis:Handbook of Series for Scientists and Engineers (Academic Press, New York, N. Y., 1965), Part II, sect. 11.zbMATHGoogle Scholar
  46. (48).
    A. Erdèlti, Editor:Higher Transcendental Functions,Vol. 1 (McGraw-Hill Book Co., Inc., New York, N. Y., 1953).Google Scholar
  47. (49).
    K. Knopp:Theorie und Anwendung der Unendlichen Reihen (Springer-Verlag, Berlin, 1964), Chapts. I and X.CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica 1986

Authors and Affiliations

  • M. H. Saffouri
    • 1
    • 2
  1. 1.International Centre for Theoretical PhysicsTriesteItaly
  2. 2.International School for Advanced StudiesTriesteItaly

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