Regularity of constraints and reduction in the Minkowski space Yang-Mills-Dirac theory
Śniatycki, Jedrzej
Annales de l'I.H.P. Physique théorique, Tome 71 (1999), p. 277-293 / Harvested from Numdam
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Publié le : 1999-01-01
@article{AIHPA_1999__70_3_277_0,
     author = {\'Sniatycki, J\k edrzej},
     title = {Regularity of constraints and reduction in the Minkowski space Yang-Mills-Dirac theory},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {71},
     year = {1999},
     pages = {277-293},
     mrnumber = {1718183},
     zbl = {0958.58009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1999__70_3_277_0}
}

Śniatycki, Jedrzej. Regularity of constraints and reduction in the Minkowski space Yang-Mills-Dirac theory. Annales de l'I.H.P. Physique théorique, Tome 71 (1999) pp. 277-293. http://gdmltest.u-ga.fr/item/AIHPA_1999__70_3_277_0/

[1] I. Segal, The Cauchy problem for the Yang-Mills equations, J. Funct. Anal., Vol. 33, 1979, pp. 175-194. | MR 546505 | Zbl 0416.58027

[2] J. Ginibre and G. Velo, The Cauchy problem for coupled Yang-Mills and scalar fields in the temporal gauge, Commun. Math. Phys., Vol. 82, 1981, pp. 1-28. | MR 638511 | Zbl 0486.35048

[3] J. Ginibre and G. Velo, The Cauchy problem for coupled Yang-Mills and scalar fields in the Lorentz gauge, Ann. Inst. H. Poincaré, Vol. 36, 1982, pp. 59-78. | Numdam | MR 653018 | Zbl 0486.35049

[4] D.M. Eardley and V. Moncrief, The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space, Comm. Math. Phys., Vol. 83, 1982, pp. 171-191. | MR 649158 | Zbl 0496.35061

[5] D.M. Eardley and V. Moncrief, The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space, Comm. Math. Phys., Vol. 83, 1982, pp. 193-212. | MR 649159 | Zbl 0496.35062

[6] Y. Choquet-Bruhat and D. Christodoulou, Existence of global solutions of the Yang-Mills, Higgs and spinor field equations in 3+1 dimensions, Ann. Sci. École Norm. Sup., Vol. 14, 1981, pp. 481-506. | Numdam | MR 654209 | Zbl 0499.35076

[7] S. Klainerman and M. Machedon, Finite energy solutions of the Yang-Mills equations in R3+1, Ann. Math., Vol. 142, 1995, pp. 39-119. | MR 1338675 | Zbl 0827.53056

[8] V. Moncrief, Gribov degeneracies: Coulomb gauge condition and initial value constraints, J. Math. Phys., Vol. 20, 1979, pp. 579-585. | MR 529721 | Zbl 0416.58008

[9] G. Schwarz and J. Śniatycki, Gauge symmetries of an extended phase space for Yang-Mills and Dirac fields, Ann. Inst. Henri Poincaré, Vol. 66, 1996, pp. 109-136. | Numdam | MR 1434116 | Zbl 0889.58089

[10] S. Lang, Differential and Riemannian Manifolds, Springer, New York, 1995. | MR 1335233 | Zbl 0824.58003

[11] T. Kato, Perturbation Theory for Linear Operators, Springer Verlag, Berlin, Heidelberg, New York, 1984.

[12] J. Śniatycki, Regularity of constraints in the Minkowski space Yang-Mills theory, Comm. Math. Phys., Vol. 141, 1991, pp. 593-597. | MR 1134941 | Zbl 0734.53026

[13] J. Śniatycki, G. Schwarz and L. Bates, Yang-Mills and Dirac fields in a bag, constraints and reduction, Comm. Math. Phys., Vol. 176, 1996, pp. 95-115. | MR 1372819 | Zbl 0852.58080

[14] P. Mitter and C. Viallet, On the bundle of connections and the gauge orbit manifold in Yang-Mills theory, Comm. Math. Phys., Vol. 79, 1981, pp. 457-472. | MR 623962 | Zbl 0474.58004

[15] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 2, Academic Press, New York, 1975.

[16] R. Adams, Sobolev Spaces, Academic Press, Orlando, Florida, 1975. | Zbl 0314.46030

[17] K. Uhlenbeck, Removable singularities in Yang-Mills fields, Comm. Math. Phys., Vol. 83, 1982, pp. 11-29. | MR 648355 | Zbl 0491.58032

[18] R. Palais, On the existence of slices for actions of non-compact Lie groups, Ann. Math., Vol. 73, 1961, pp. 295-323. | MR 126506 | Zbl 0103.01802

[19] J. Arms, J.E. Marsden and V. Moncrief, Symmetry and bifurcation of momentum maps, Comm. Math. Phys., Vol. 90, 1981, pp. 361-372.

[20] R. Cushman and L. Bates, Global Aspects of Classical Integrable Systems, Birkhäuser Verlag, Basel, Boston, Berlin, 1997. | MR 1438060 | Zbl 0882.58023