Gauge symmetries of an extended phase space for Yang-Mills and Dirac fields
Schwarz, Günter ; Śniatycki, Jędrzej
Annales de l'I.H.P. Physique théorique, Tome 67 (1997), p. 109-136 / Harvested from Numdam
@article{AIHPA_1997__66_1_109_0,
     author = {Schwarz, G\"unter and \'Sniatycki, J\k edrzej},
     title = {Gauge symmetries of an extended phase space for Yang-Mills and Dirac fields},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {67},
     year = {1997},
     pages = {109-136},
     mrnumber = {1434116},
     zbl = {0889.58089},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1997__66_1_109_0}
}
Schwarz, Günter; Śniatycki, Jędrzej. Gauge symmetries of an extended phase space for Yang-Mills and Dirac fields. Annales de l'I.H.P. Physique théorique, Tome 67 (1997) pp. 109-136. http://gdmltest.u-ga.fr/item/AIHPA_1997__66_1_109_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. Ginebre and G. Velo, "The Cauchy problem for coupled Yang-Mills and scalar fields in temporal gauge", Comm. Math. Phys., Vol. 82, 1981, pp. 1-28. | MR 638511 | Zbl 0486.35048

[3] 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 and pp. 193-212. | Zbl 0496.35061

[4] Y. Choquet-Bruhat and D. Christodoulu, "Exitence de solutions globales deséquations classiques des théories de jauge", C. R. Acad. Sc. Paris, Vol. 293, sér.1, 1981, pp. 181-195. | Zbl 0478.58027

[5] S. Klainerman and M. Machedon, "Finite energy solutions of the Yang-Mills equations in IR3+1", preprint, Department of Mathematics, Princeton University.

[6] R.A. Adams, Sobolev Spaces, Academic Press, Orlando, Florida, 1975. | MR 450957 | Zbl 0314.46030

[7] H. Aikawa, "On weighted Beppo Levi functions. Integral representation and behaviour at infinity", Analysis, Vol. 9, 1989, pp. 323-346. | MR 1032579 | Zbl 0697.31004

[8] J. Deny and J.L. Lions, "Les éspaces du type de Beppo Levi", Ann. Inst. Fourier, Vol. 5, 1955, pp. 305-370. | Numdam | MR 74787 | Zbl 0065.09903

[9] R. Mcowen, "The behavior of the Laplacian on weighted Sobolev spaces", Comm. Pure Appl. Math., Vol. XXXII, 1979, pp. 783-795. | MR 539158 | Zbl 0426.35029

[10] G. Schwarz, Hodge Decomposition - A Method for Solving Boundary Value Problems, Lecture Notes in Mathematics 1607, Springer-Verlag, Heidelberg, 1995. | MR 1367287 | Zbl 0828.58002

[11] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, 1983. | MR 710486 | Zbl 0516.47023

[12] J. Weidmann, Linear Operators in Hilbert Spaces, Springer Verlag, Berlin, 1980. | MR 566954 | Zbl 0434.47001

[13] K. Yosida, Functional Analysis, Springer Verlag, Berlin, 1971. | Zbl 0217.16001

[14] G. Schwarz and J. Śniatycki, "Yang-Mills and Dirac fields in a bag, existence and uniqueness theorems", Comm. Math. Phys., Vol. 168, 1995, pp. 441-453. | MR 1324405 | Zbl 0826.53057

[15] 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. 95-117. | MR 1372819 | Zbl 0852.58080

[16] I. Segal, "Non-linear semigroups", Ann. Math., Vol. 78, 1963, pp. 339-364. | MR 152908 | Zbl 0204.16004

[17] G. Schwarz and J. Śniatycki, "The Hamiltonian evolution of Yang-Mills and Dirac fields", Acta Phys. Pol. B 27, No. 4, 1-12 (1996).

[18] W. Von Wahl, "Analytische Abbildungen und semilineare Differentialgleichungen in Banachräumen", Nachr. Akad. Wiss. Göttingen, II, math.-phys. Klasse, 1979, pp. 1-48. | MR 568805 | Zbl 0433.34047

[19] J. Eichhorn, "Gauge theory of open manifolds of bounded geometry", Ann. Global Anal. Geom., Vol. 11, 1993, pp. 253-300. | MR 1175322

[20] A. Weil, Sur les espaces a structures uniformes, Act. Sci. Ind., 551, Hermann, Paris, 1938. | Zbl 0019.18604

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

[22] G. Schwarz and J. Śniatycki, "The constraint set of the Yang-Mills-Dirac theory in the Minkowski space", in preparation.

[23] J. Śniatycki and G. Schwarz [94], "An invariance argument for confinement", Rep. Math. Phys., 34, 1994, pp. 311-324. | MR 1339468 | Zbl 0831.58056

[24] C. Amrouche, V. Girault and J. Giroire, "Weighted Sobolev spaces for Laplace's equation in IRn", J. Math. Pures Appl., Vol. 73, 1994, pp. 579-606. | MR 1309165 | Zbl 0836.35038