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Path-ordered phase factors as generators of gauge fields

Фазовые множители, упорядоченные по траекториям, как генераторы калибровочных полей

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Il Nuovo Cimento A (1965-1970)

Summary

A new method to construct the gauge fields is developed. The gauge fields are derived mathematically as the necessary consequence from only a few postulates which have physical images. It is shown that the path-ordered phase factors satisfy these postulates and are the representation of the linear Lie group.

Riassunto

Si sviluppa un nuovo metodo per costruire i campi di gauge. I campi di gauge sono derivati matematicamente come conseguenza neoessaria di solo pochi postulati che hanno rappresentazioni fisiche. Si mostra che i fattori di fase ordinati secondo il percorso soddisfano questi postulati e sono la rappresentazione del gruppo lineare di Lie.

Резюме

Развивается новый метод конструирования калибровочных полей. Калибровочные поля выводятся математически, как необходимое следствие из нескольких постулатов, которые имеют фуизические образы. Показывается, что фазовые множители, упорядоченные по траекториям, удовлетворяют этим постулатам и являются представлением линейной группы Ли.

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References

  1. E. Utiyama:Prog. Theor. Phys.,64, 2207 (1980).

    Article  ADS  Google Scholar 

  2. H. Weyl:Z. Phys.,56, 330 (1929).

    Article  ADS  Google Scholar 

  3. R. Utiyama:Phys. Rev.,101, 1597 (1956).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. A. Trautman:Symp. Math.,12, 139 (1973).

    MathSciNet  Google Scholar 

  5. C. N. Yang:Phys. Rev. Lett.,33, 445 (1974).

    Article  MathSciNet  ADS  Google Scholar 

  6. I. Ojima:Soryusiron Kenkyū,53–4, 299 (1976–7) (mimeographed circular in Japanese);W. Drechsler andM. E. Mayer:Fiber bundle techniques in gauge theories, inLecture Notes in Physics, Vol. 67 (Berlin, Heidelberg and New York, N. Y., 1977);S. Kobayashi andK. Nomizu:Foundations of Differential Geometry (New York, N. Y., and London, 1963);J. L. Koszul:Lectures on Fibre Bundles and Differential Geometry (Bombay, 1960).

    Google Scholar 

  7. S.-S. Chern:Geometry of characteristic classes, inProceedings of the XIII Biennial Seminar, Canadian Mathematical Congress (1972), p. 1.

  8. M. Itanaga:Tech. Rep. Yamaguchi Univ.,2, 431 (1980).

    Google Scholar 

  9. E. Corrigan andB. Hasslacher:Phys. Lett. B,81, 181 (1979).

    Article  ADS  Google Scholar 

  10. T. T. Wu andC. N. Yang:Phys. Rev. D,12, 3845 (1975).

    Article  MathSciNet  ADS  Google Scholar 

  11. O. M. Khudaverdian andA. S. Schwarz:Phys. Lett. B,91, 107 (1980);A. M. Polyakov:Nucl. Phys. B,164, 171 (1979).

    Article  ADS  Google Scholar 

  12. M. Iyanaga:Generalization of Stokes theorem and pure gauge fields, to be published inJ. Math. Phys. (N. Y.).

  13. H. Weyl:Raum, Zeit, Materie (Tokyo, 1972, Japanese translation).

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Authors and Affiliations

  1. Faculty of Engineering, Yamaguchi University, 755, Tokiwadai, Ube, Japan

    M. Iyanaga

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  1. M. Iyanaga
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Iyanaga, M. Path-ordered phase factors as generators of gauge fields. Nuov Cim A 71, 187–204 (1982). https://doi.org/10.1007/BF02816728

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  • DOI: https://doi.org/10.1007/BF02816728

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