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Dual Lagrangian Theories

  • M. Ferraris
  • M. Raiteri
Conference paper

Abstract

The procedure for constructing dual Lagrangians depending only on canonical momenta is described. The theory is applied to explain the equivalence between certain relativistic theories of gravitation and general relativity. The theory of dual Lagrangians for gauge theories is studied in detail. As an example, we describe SO(3) and SO(2,1) Yang-Mills theories on 3-dimensional and 4-dimensional manifolds.

Keywords

Gauge Theory Vector Bundle Lagrangian Density Gauge Potential Legendre Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Ferraris M., Francaviglia M., Raiteri M. (2000): Dual Lagrangian field theories. J. Math. Phys., in pressGoogle Scholar
  2. 2.
    Ferraris M., Kijowski J. (1982): On the equivalence of relativistic theories of gravitation. Gen. Rel. Grav. 14(1), 165–180ADSMATHCrossRefGoogle Scholar
  3. 3.
    Hilbert D. (1915): Die Grundlagen der Physik. Königl. Gesel. Wiss., Göttingen Nachr., Math. Phys. Kl., 394–407Google Scholar
  4. 4.
    Einstein A. (1916): Hamiltonsches Prinzip und allgemeine Relativitätstheorie. Sitzungsber. Preuss. Akad. Wiss. (Berlin), 1111–1116Google Scholar
  5. 5.
    Einstein A. (1923): Zur allgemeinen Relativitätstheorie. Sitzungsber. Preuss. Akad. Wiss. (Berlin), 32–38Google Scholar
  6. 6.
    Einstein A. (1923): Zur affinen Feldtheorie. Sitzungsber. Preuss. Akad. Wiss. (Berlin), 137–140Google Scholar
  7. 7.
    Schrödinger E. (1943): The general unitary theory of the physical fields. Proc. R. Irish Acad. A 49, 43–58MATHGoogle Scholar
  8. 8.
    Schrödinger E. (1946): The general affine field laws. Proc. R. Irish Acad. A 51, 41–50MATHGoogle Scholar
  9. 9.
    Schrödinger E. (1947): The final affine field laws, I. Proc. R. Irish Acad. A 52, 163–171Google Scholar
  10. 10.
    Schrödinger E. (1948a): The final affine field laws, II. Proc. R. Irish Acad. A 51, 205–216Google Scholar
  11. 11.
    Schrödinger E. (1948): The final affine field laws, III. Proc. R. Irish Acad. A 52, 1–9Google Scholar
  12. 12.
    Kijowski J. (1978): On a new variational principle in general relativity and the energy of the gravitational field. Gen. Rel. Grav. 9, 857–877MathSciNetADSMATHCrossRefGoogle Scholar
  13. 13.
    Ferraris M., Kijowski J. (1981): General relativity is a Gauge-type theory. Lett. Math. Phys. 5, 127–135MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    Ferraris M., Kijowski J. (1982): Unified geometric theory of electromagnetic and gravitational interactions. Gen. Rel. Grav. 14(1), 37–47MathSciNetADSMATHCrossRefGoogle Scholar
  15. 15.
    Ferraris M. (1984): Affine Unified Theories of Gravitation and Electromagnetism, in Proc. Journées Relativistes 1983 (Torino, 1983), ed. by S. Benetti, M. Ferraris, M. Francaviglia, Tecnoprint, Bologna, pp. 125–153Google Scholar
  16. 16.
    Raiteri M., Ferraris M., Francaviglia M. (1996): General Relativity as a Gauge Theory of Orthogonal Groups in Three Dimensions, in Gravity, Particles and Space-Time, ed. by Pronin P. and Sardanashvily G., World Scientific, Singapore, pp. 81–98CrossRefGoogle Scholar
  17. 17.
    Ferraris M., Francaviglia M., Raiteri M.: Dual Lagrangian Formulation of Gauge Theories, in preparationGoogle Scholar
  18. 18.
    Urbantke H. (1984): J. Math. Phys. 25, 2321MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    Lunev F.A. (1992): Phys. Lett. B 295, 99MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    Bengtsson I. (1995): Class. Quantum Grav. 12, 1581MathSciNetADSMATHCrossRefGoogle Scholar
  21. 21.
    Ganor O., Sonnenschein J. (1995): hep-th/9507036Google Scholar
  22. 22.
    Capovilla R., Jacobson T., Dell J. (1989): Phys. Rev. Lett. 63, 2325MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    Capovilla R., Jacobson T., Dell J., Mason L. (1991): Class. Quantum Grav. 8, 41MathSciNetADSMATHCrossRefGoogle Scholar
  24. 24.
    Capovilla R., Jacobson T., Dell J. (1991): Class. Quantum Grav. 8, 59MathSciNetADSMATHCrossRefGoogle Scholar
  25. 25.
    Capovilla R., Jacobson T. (1992): Modern Phys. Lett. A 7(21), 1871MathSciNetADSMATHCrossRefGoogle Scholar
  26. 26.
    Ashtekar A. (1988): New Perspectives in Canonical Gravity. Bibliopolis, NapoliMATHGoogle Scholar
  27. 27.
    Fatibene L., Ferraris M., Francaviglia M., Raiteri M. (1999): Phys. Rev. D 60, 124013MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2000

Authors and Affiliations

  • M. Ferraris
  • M. Raiteri

There are no affiliations available

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