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On the Hamiltonian Formulation of Gauge Theories in Terms of Physical Variables

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REFERENCES

  1. V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt, “Mathematical aspects of classical and celestial mechanics,” In: Dynamical Systems, 3, Springer-Verlag, New York-Berlin (1988).

    Google Scholar 

  2. R. Arnowitt, S. Deser, and C. W. Misner, J. Math. Phys., 1, 434 (1960).

    Google Scholar 

  3. H. M. Asatryan and G. K. Savvidy, Phys. Lett. A, 99, 290 (1983).

    Google Scholar 

  4. M. F. Atyah, Geometry of Yang-Mills Fields, Sc. Norm. Super., Pisa (1979).

    Google Scholar 

  5. O. Azuma and S. Iso, Phys. Lett. B, 331, 107–113 (1994).

    Google Scholar 

  6. O. Babelon and M. Talon, Phys. Lett. A, 236, 462–468 (1997).

    Google Scholar 

  7. O. Babelon and C. M. Viallet, Commun. Math. Phys., 81, 515 (1981).

    Google Scholar 

  8. V. Baluni and B. Grossman, Phys. Lett. B, 78, 226 (1978).

    Google Scholar 

  9. I. A. Batalin and G. A. Vilkovisky, Nucl. Phys. B, 234, 106 (1984).

    Google Scholar 

  10. M. Bauer, D. Z. Freedman, and P. E. Haagensen, Nucl. Phys. B, 428, 147 (1994).

    Google Scholar 

  11. A. A. Belavin, A. M. Polyakov, A. S. Schwartz, and Yu. S. Tyupkin, Phys. Lett. B, 59, 85 (1975).

    Google Scholar 

  12. P. G. Bergman and I. Goldberg, Phys. Rev., 98, 531 (1955).

    Google Scholar 

  13. J. Blom and E. Langmann, Phys. Lett. B, 429, 336–342 (1998).

    Google Scholar 

  14. A. Bohr and B. R. Mottelson, Nuclear Structure, Vol. 2, Benjamin (1975).

  15. L. Brink, T. H. Hansson, S. Konstein, and M. A. Vasiliev, Nucl. Phys. B, 401, 591–612 (1993).

    Google Scholar 

  16. D. M. Brink and G. R. Satcheler, Angular Momentum, Oxford Univ. Press, Oxford (1993).

    Google Scholar 

  17. C. G. Callan, R. F. Dashen, and D. J. Gross, Phys. Lett. B, 63, 334 (1976).

    Google Scholar 

  18. F. Calogero, J. Math. Phys., 10, 2191–2196 (1969).

    Google Scholar 

  19. F. Calogero, J. Math. Phys., 10, 2197–2200 (1969).

    Google Scholar 

  20. F. Calogero, J. Math. Phys., 12, 419–436 (1972).

    Google Scholar 

  21. E. Cartan, Leçons sur les Invariant Integraux, Hermann, Paris (1922).

    Google Scholar 

  22. G. Chechelashvili, G. Jorjadze, and N. Kiknadze, “Practical scheme of reduction to gauge invariant variables,” Teor. Mat. Fiz., 109,No. 1, 90 (1997).

    Google Scholar 

  23. N. H. Christ and T. D. Lee, Phys. Rev., 22, 939 (1980).

    Google Scholar 

  24. M. Creutz, I. J. Muzinich, and T. N. Tudron, Phys. Rev., 19, 531 (1979).

    Google Scholar 

  25. E. D'Hoker and D. H. Phong, Nucl. Phys. B, 530, 537–610 (1998).

    Google Scholar 

  26. E. D'Hoker and D. H. Phong, Nucl. Phys. B, 530, 611–640 (1998).

    Google Scholar 

  27. E. D'Hoker and D. H. Phong, Nucl. Phys. B, 534, 697–719 (1998).

    Google Scholar 

  28. E. D'Hoker and D. H. Phong, Lectures on supersymmetric Yang-Mills theory and integrable systems, Preprint hep-th/991271.

  29. E. D'Hoker and D. H. Phong, Seiberg-Witten theory and integrable systems, Preprint hep-th/9903068.

  30. B. Dahmen, B. Raabe, Nucl. Phys. B, 384, 352 (1992).

    Google Scholar 

  31. A. Das, M. Kaku, and P. K. Townsend, Nucl. Phys. B, 149, 109 (1979).

    Google Scholar 

  32. S. Deser, R. Jackiw, and S. Templeton, Ann. Phys., 140, 372 (1982).

    Google Scholar 

  33. P. A. M. Dirac, Rev. Mod. Phys., 21, 392 (1949).

    Google Scholar 

  34. P. A. M. Dirac, Proc. Roy. Soc. A, 246, 333 (1958).

    Google Scholar 

  35. P. A. M. Dirac, Phys. Rev., 114, 924 (1959).

    Google Scholar 

  36. P. A. M. Dirac, Phys. Rev., 114, 924 (1959).

    Google Scholar 

  37. P. A. M. Dirac, Phys. Rev. Lett., 2368 (1959).

  38. P. A. M. Dirac, Lectures on Quantum Mechanics, New York (1964).

  39. R. Donagi and E. Witten, Nucl. Phys. B, 460, 288–334 (1996).

    Google Scholar 

  40. L. D. Faddeev, Teor. Mat. Fiz., 1, 1 (1969).

    Google Scholar 

  41. L. D. Faddeev and A. J. Niemi, “Partially dual variables in SU(2) Yang-Mills theory,” Phys. Rev. Lett., 82, 1624 (1999).

    Google Scholar 

  42. L. D. Faddeev and A. A. Slavnov, Gauge Fields: Introduction to Quantum Theory, Benjamin (1984).

  43. V. Fock, Z. Phys., 39, 226–232 (1926).

    Google Scholar 

  44. G. W. Gibbons and P. K. Townsend, Preprint hep-th/9812034.

  45. J. Gibbons and T. Hermsen, Physica D, 11, 337–348 (1984).

    Google Scholar 

  46. V. N. Gribov, Nucl. Phys. B, 139, 1 (1978).

    Google Scholar 

  47. S. A. Gogilidze, A. M. Khvedelidze, D. M. Mladenov, and H.-P. Pavel, Phys. Rev. D, 57, 7488 (1998).

    Google Scholar 

  48. S. A. Gogilidze, A. M. Khvedelidze, and V. N. Pervushin, J. Math. Phys., 37, 1760 (1996).

    Google Scholar 

  49. S. A. Gogilidze, A. M. Khvedelidze, and V. N. Pervushin, Phys. Rev. D, 53, 2160 (1996).

    Google Scholar 

  50. S. A. Gogilidze, V. N. Pervushin, and A. M. Khvedelidze, “Reduction in systems with local symmetry,” Phys. Part. Nucl., 30, 66 (1999).

    Google Scholar 

  51. J. Goldstone and R. Jackiw, Phys. Lett. B, 74, 81 (1978).

    Google Scholar 

  52. A. Gorsky and N. Nekrasov, Nucl. Phys. B, 414, 213–238 (1994).

    Google Scholar 

  53. A. Gorsky and N. Nekrasov, Elliptic Calogero-Moser systems from two-dimensional current algebra, Preprint hep-th/9401021.

  54. M. J. Gotay, J. Geom. Phys., 6, 349 (1989).

    Google Scholar 

  55. P. E. Haagensen and K. Johnson, Nucl. Phys. B, 439, 597 (1995).

    Google Scholar 

  56. F. D. M. Haldane, Phys. Rev. Lett., 60, 635–638 (1988).

    Google Scholar 

  57. K. Haller, Phys. Rev. D, 36, 1839 (1987).

    Google Scholar 

  58. M. Henneaux and C. Teitelboim, Quantization of Gauge Systems, Princeton Univ. Press, Princeton, New Jersey (1992).

    Google Scholar 

  59. H. Itoyama and A. Morozov, Integrability and Seiberg-Witten theory, Preprint hep-th/9601168.

  60. A. G. Izergin, V, F. Korepin, M. E. Semenov-Tyan-Shanskii, and L. D. Faddeev, Teor. Mat. Fiz., 38, 3 (1979).

    Google Scholar 

  61. R. Jackiw, “Topological investigations of quantized gauge theories,” In: Current Algebra and Anomalies, World Scientific, Singapore (1985).

    Google Scholar 

  62. R. Jackiw and C. Rebbi, Phys. Rev. Lett., 37, 172 (1976).

    Google Scholar 

  63. J. D. Jackson and L. B. Okun, “Historical roots of gauge invariance,” Rev. Mod. Phys., 73, 663 (2001).

    Google Scholar 

  64. N. Kawakami, Phys. Rev. Lett., 71, 275–278 (1993).

    Google Scholar 

  65. A. M. Khvedelidze and D. M. Mladenov, “Euler-Calogero-Moser system from SU(2) Yang-Mills theory,” Phys. Rev. D, 62 (2000).

  66. A. M. Khvedelidze and H.-P. Pavel, “Nonperturbative reduction of Yang-Mills theory and lowenergy effective action,” In: Proc. Int. Sem. Phys. Math., Tbilisi, Georgia, 5–18 Sept. 1998, Tbilisi (1998), pp. 205–216.

  67. A. M. Khvedelidze and H.-P. Pavel, “Unconstrained Hamiltonian formulation of SU(2) gluodynamics,” Phys. Rev. D, 59 (1999).

  68. A. M. Khvedelidze and H.-P. Pavel, “On the groundstate of Yang-Mills quantum mechanics,” Phys. Lett. A, 267, 96 (2000).

    Google Scholar 

  69. A. M. Khvedelidze and V. N. Pervushin, Helv. Phys. Acta, 67,No. 6, 637 (1994).

    Google Scholar 

  70. O. Klein, “On the theory of charged fields,” In: New Theories in Physics. Proc. Conf. Int. Union of Physics and the Polish Intellectual Cooperation Committee. Warsaw, May 30–June 3, 1938.

  71. I. I. Kogan and A. Kovner, Phys. Rev. D, 52, 3719 (1995).

    Google Scholar 

  72. I. M. Krichever, O. Babelon, E. Billey, and M. Tallon, Am. Math. Soc. Transl., 150, 83–119 (1995).

    Google Scholar 

  73. I. M. Krichever and D. H. Phong, On the integrable geometry of soliton equations and the N = 2 supersymmetric gauge theories, Preprint hep-th/9604199.

  74. M. Kuś, F. Haake, D. Zaitsev, and A. Huckleberry, J. Phys. A: Math. Gen., 30, 8635–8651 (1997).

    Google Scholar 

  75. E. Langmann, M. Salmhofer, and A. Kovner, Mod. Phys. Lett. A, 9, 2913–2926 (1994).

    Google Scholar 

  76. E. Langmann and G. Semenoff, Phys. Lett. B, 296, 117–120 (1992).

    Google Scholar 

  77. M. Lavelle and D. McMullan, Phys. Rep., 279, 1 (1997).

    Google Scholar 

  78. J. M. Leinaas, “Topological charges in gauge theories,” Fortsch. Phys., 28, 579 (1980).

    Google Scholar 

  79. J. M. Leinaas, Generalized statistics and the algebra of observables, Preprint hep-th/9611167.

  80. F. London, Naturwiss., 15, 187 (1927).

    Google Scholar 

  81. F. London, Z. Phys., 42, 375–389 (1927).

    Google Scholar 

  82. H. Loos, Phys. Rev., 188, 2342 (1969).

    Google Scholar 

  83. M. Luesher, Nucl. Phys., 219, 233 (1983).

    Google Scholar 

  84. M. Marcus and H. Minc, A Survey of Matrix Theory and Matrix Inequalities, Allyn and Bacon, Boston (1964).

    Google Scholar 

  85. J. Marsden and A. Weinstein, Rep. Math. Phys., 5, 121 (1974).

    Google Scholar 

  86. D. Martin, Manifold Theory, Ellis Horwood, Chichester (1991).

    Google Scholar 

  87. C. Martin and D. Vautherin, “Ground state properties and glueball spectrum,” In: Yang-Mills Theory Using Gauge Invariant Variables, Orsay Preprint IPNO/TH 93–68 (1993) (unpublished).

  88. E. Martinec, Integrable structures in supersymmetric gauge and string theory, Preprint hep-th/9510204.

  89. S. G. Matinyan, G. K. Savvidy, and N. G. Ter-Arutyunyan-Savvidy, Sov. Phys. JETP, 53, 421 (1981).

    Google Scholar 

  90. J. A. Minahan and A. P. Polychronakos, Phys. Lett. B, 326, 288–294 (1994).

    Google Scholar 

  91. P. K. Mitter, In: Recent Developments in Gauge Theories (G. t'Hooft, Ed.), Plenum Press, New York (1980).

    Google Scholar 

  92. V. Moncrief, Lect. Notes Math., 836, 276 (1980).

  93. J. Moser, Adv. Math., 16, 197–220 (1975).

    Google Scholar 

  94. H. Nachgebauer, Phys. Rev. D, 52, 3672 (1995).

    Google Scholar 

  95. M. S. Narasimhan, T. R. Ramadas, Commun. Math. Phys., 67, 21 (1979).

    Google Scholar 

  96. E. T. Newman and C. Rovelli, Phys. Rev. Lett., 69, 1300 (1992).

    Google Scholar 

  97. L. O'Raifeartaigh and N. Straumann, “Gauge theory: Historical origins and some modern developments,” Rev. Mod. Phys., 72 (2000).

  98. M. A. Olshanetsky and A. M. Perelomov, Phys. Rep., 71, 313–400 (1981).

    Google Scholar 

  99. M. A. Olshanetsky and A. M. Perelomov, Phys. Rep., 94, 313–404 (1983).

    Google Scholar 

  100. P. Olver, Applications of Lie Groups to Differential Equations, Grad. Texts Math., Springer-Verlag, New York (1986).

    Google Scholar 

  101. A. M. Perelomov, Lett. Math. Phys., 1, 531–540 (1977).

    Google Scholar 

  102. A. M. Perelomov, Integrable Systems in Classical Mechanics and Lie Algebra [in Russian], Nauka, Moscow (1990).

    Google Scholar 

  103. V. N. Pervushin, Teor. Mat. Fiz., 45, 327 (1980).

    Google Scholar 

  104. A. P. Polychronakos, Generalized statistics in one dimension, Preprint hep-th/9902157.

  105. A. P. Polychronakos, Nucl. Phys. B, 543, 485–498 (1999).

    Google Scholar 

  106. L. V. Prokhorov, “Phase space in theories with a gauge group,” Yad. Fiz., 35, 229 (1982).

    Google Scholar 

  107. L. V. Prokhorov, Phys. Particles Nuclei, 31 (2000).

  108. R. Schiappa, Nucl. Phys. B, 517, 462 (1998).

    Google Scholar 

  109. N. Seiberg and E. Witten, Nucl. Phys. B, 426, 19–52 (1994).

    Google Scholar 

  110. N. Seiberg and E. Witten, Nucl. Phys. B, 431, 484–550 (1994).

    Google Scholar 

  111. S. Shanmugadhasan, J. Math. Phys., 14, 677 (1973).

    Google Scholar 

  112. B. S. Shastry, Phys. Rev. Lett., 60, 639–642 (1988).

    Google Scholar 

  113. Yu. Simonov, Sov. J. Nucl. Phys., 41, 835 (1985).

    Google Scholar 

  114. I. M. Singer, Commun. Math. Phys., 60, 7 (1978).

    Google Scholar 

  115. I. M. Singer, Physica Scripta, 24, 817 (1981).

    Google Scholar 

  116. M. A. Soloviev, Teor. Mat. Fiz., 73, 3 (1987).

    Google Scholar 

  117. K. Sundermeyer, Constrained Dynamics, Lect. Notes Phys., Vol. 169, Springer-Verlag, Berlin-Heidelberg-New York (1982).

    Google Scholar 

  118. B. Sutherland, Phys. Rev. A, 4, 2019–2021 (1971).

    Google Scholar 

  119. B. Sutherland, Phys. Rev. A, 5, 1372–1376 (1972).

    Google Scholar 

  120. A. N. Tavkhelidze, “Color, colored quarks, quantum chromodynamics,” In: Proc. Int. Sem. Quarks 94, Vladimir, Russia, May 1994; Preprint JINR-E2–94–372, Dubna (1994).

  121. M. A. Vasiliev, Phys. Lett. B, 285, 225–234 (1992).

    Google Scholar 

  122. V. V. Vlasov, V. A. Matveev, A. N. Tavkhelidze, S. Yu. Khlebnikov, and M. E. Shaposhnikov, Phys. Elem. Part. Nucl., 18, 5 (1987).

    Google Scholar 

  123. H. Weyl, “Eine neue Erweiterung der Relativitätstheorie,” Ann. Phys., 59, 101–133 (1919).

    Google Scholar 

  124. H. Weyl, “Elektron und Gravitation,” Z. Phys., 56, 330–352 (1929).

    Google Scholar 

  125. E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge Univ. Press, Cambridge (1937).

    Google Scholar 

  126. S. Wojciechowski, Phys. Lett. A, 111, 101–103 (1985).

    Google Scholar 

  127. C. N. Yang, “Hermann Weyl's contributions to physics,” In: Hermann Weyl, 1885–1985, (K. Chandrasekharan, Ed.), Springer-Verlag, Berlin (1986), pp. 7–21.

    Google Scholar 

  128. C. N. Yang and R. L. Mills, Phys. Rev., 96, 191 (1954).

    Google Scholar 

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Khvedelidze, A.M. On the Hamiltonian Formulation of Gauge Theories in Terms of Physical Variables. Journal of Mathematical Sciences 119, 513–555 (2004). https://doi.org/10.1023/B:JOTH.0000009374.82259.de

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