Michel theory of symmetry breaking and gauge theories

Annals of Physics

Volumn 260, Issue 1, 1997, Pages 149-170

  Gaeta, Giuseppe ^a,c   Morando, Paola ^b  

^a INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

^b POLITECNICO DI TORINO   (Italy)

^c LOUGHBOROUGH UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031256517     PISSN: 00034916     EISSN: None     Source Type: Journal    
DOI: 10.1006/aphy.1997.5700     Document Type: Article

References (82)

1. Michel L. Points critiques de fonctions invariantes sur une G-variété C. R. Acad. Sci. Paris A. 272:1971;433-436.
2. 3. Evolution of particle Physics (E. Amaldi Festschrift). 1970;Academic Press, New York. p. 191-203.
3. Michel L., Radicati L. Properties of the breaking of hadronic internal symmetry. Ann. Phys. (N.Y.). 66:1971;758-783.
4. Michel L., Radicati L. The geometry of the octet. Ann. I.H.P. 18:1973;185.
5. Michel L. Nonlinear group action. Smooth action of compact Lie groups on manifolds. Sen R. N., Weil C. Statistical Mechanics and Field Theory. 1971;Israel Univ. Press, Jerusalem.
6. Michel L. Les brisure spontanées de symétrie en physique. J. Phys. (Paris). 36:1975;41.
7. Michel L. Symmetry defects and broken symmetry. Configurations. Hidden symmetry. Rev. Mod. Phys. 52:1980;617-651.
8. Abud M., Sartori G. The geometry of orbit space and natural minima of Higgs potentials. Phys. Lett. B. 104:1981;147-152.
9. Abud M., Sartori G. The geometry of spontaneous symmetry breaking. Ann. Phys. 150:1983;307-372.
10. Sartori G., Talamini V. Universality in orbit spaces of compact linear groups. Comm. Math. Phys. 139:1991;559-588.
11. Sartori G., Valente G. Orbit spaces of reflection groups with 2, 3, and 4 basic polynomial invariants. J. Phys. A. 29:1996;193-223.
12. Sartori G. Geometric invariant theory. A model-independent approach to spontaneous symmetry and/or supersymmetry breaking. Riv. N. Cim. 14:(1991);1-120.
13. Field M. J., Richardson R. W. Symmetry-breaking and the maximal isotropy subgroup conjecture for reflection groups. Arch. Rat. Mech. Anal. 105:1989;61-94.
14. M. J. Field, R. W. Richardson, Symmetry-breaking in equivariant bifurcation problems, Bull. Amer. Math. Soc. 22, 79, 84.
15. Field M. J., Richardson R. W. Symmetry-breaking and branching patterns in equivariant bifurcation theory, I. Arch. Rat. Mech. Anal. 118:1992;297-348.
16. Field M. J., Richardson R. W. Symmetry-breaking and branching patterns in equivariant bifurcation theory, II. Arch. Rat. Mech. Anal. 120:1992;147-190.
17. Bredon G. Compact transformation groups. 1972;Academic Press, New York/London.
18. Field M. J. Symmetry breaking for compact Lie groups. Mem. Amer. Math. Soc. 120:1996;1-170.
19. Gaeta G. Michel's theorem and critical section of gauge functionals. Helv. Phys. Acta. 65:1992;922-964.
20. Gaeta G. Critical sections of gauge functionals: a symmetry approach. Lett. Math. Phys. 28:1993;1-11.
21. Gaeta G. Equivariant branching lemma: dynamical systems, evolution PDEs, and gauge theories. Acta Appl. Math. 28:1992;43-68.
22. Singer I. M. Some remarks on the Gribov ambiguity. Comm. Math. Phys. 60:1978;7-12.
23. Singer I. M. The geometry of the orbit space for non-abelian gauge theories. Phys. Scripta. 24:1981;817-820.
24. Narashiman M. S., Ramadas T. R. Geometry of SU(2) gauge fields. Comm. Math. Phys. 67:1979;121-136.
25. Dell'Antonio G., Zwanziger D. Every gauge orbit passes inside the Gribov horizon. Comm. Math. Phys. 138:1981;291-299.
26. Bourguignon J. P. Une stratification de l'espace des structures riemanniennes. Comp. Math. 30:1975;1-41.
27. Kondracki W., Sadowski P. Geometric structure on the orbit space of gauge connections. J. Geom. Phys. 3:1986;421-434.
28. Kondracki W., Rogulski J. S. On the stratification of orbit space for the action of automorphisms on connections. Diss. Math. 250:1986;1-62.
29. Heil A., Papadopolous N., Reifenhauser B., Scheck F. Structure of the space of reducible connexions for Yang-Mills theories. J. Geom. Phys. 7:1990;489-505.
30. Marathe K. B., Martucci G. The geometry of gauge fields. J. Geom. Phys. 6:1989;1-106.
31. Lawson H. B. The theory of gauge fields in four dimensions. Amer. Math. Soc. 1985.
32. Bourguignon J. P., Lawson H. B. Stability and isolation phenomena for Yang-Mills fields. Comm. Math. Phys. 79:1981;189-230.
33. Bourguignon J. P., Lawson H. B., Simons J. Stability and gap phenomena for Yang-Mills fields. Proc. Natl. Acad. Sci. USA. 76:1979;1550-1553.
34. Brezis H. Analyse fonctionelle. 1983;Masson, Paris.
35. Mitter P. K., Viallet C. M. On the bundle of connections and the gauge orbit manifold in Yang-Mills theory. Comm. Math. Phys. 79:1981;457-472.
36. Sniatycki J., Schwarz G., Bates L. Yang-Mills and Dirac fields in a bag, constraints and reduction. Comm. Math. Phys. 176:1996;95-115.
37. Isham C. J. Space-time topology and spontaneous symmetry breaking. J. Phys. A. 14:1981;2943-2956.
38. Atiyah M. F., Jones J. D. S. Topological aspects of Yang-Mills theory. Comm. Math. Phys. 61:1978;97-118.
39. Yang C. N., Mills R. L. Yang. Phys. Rev. 96:1954;191-195.
40. Abers E. S., Lee B. W. Gauge theories. Phys. Rep. 9:1973;1-141.
41. Eguchi T., Gilkey P. B., Hanson A. J. Gravitation, gauge theories, and differential geometry. Phys. Rep. 66:1980;213-393.
42. Drechsler W., Mayer M. E. Fibre Bundle Techniques in Gauge Theories. Lect. Notes Phys. 67:1977;Springer-Verlag, New York/Berlin.
43. Daniel M., Viallet C. M. The geometrical setting of gauge theories of Yang-Mills type. Rev. Mod. Phys. 52:1980;175-197.
44. Isham C. J. Modern differential geometry for physicists. World Scientific. 1989.
45. Palais R. S., Terng C. L. Critical point theory and submanifold geometry. Lect. Notes Math. 1353:1988;Springer-Verlag, New York/Berlin.
46. Gaeta G. A splitting lemma for equivariant dynamics. Lett. Math. Phys. 33:1995;313-320.
47. Gaeta G. Splitting equivariant dynamics. Nuovo Cimento B. 110:1995;1213-1226.
48. Cicogna G. Symmetry breakdown from bifurcation. Lett. Nuovo Cimento. 31:1981;600-602.
49. Vanderbauwhede A. Local Bifurcation and Symmetry. 1982;Pitman, Boston.
50. Cicogna G. A nonlinear version of the equivariant bifurcation lemma. J. Phys. A. 23:1990;L1339-L1343.
51. Golubitsky M., Stewart I. N. Hopf bifurcation in the presence of symmetry. Arch. Rat. Mech. Anal. 87:1985;107-165.
52. Golubitsky M., Schaeffer D., Stewart I. Singularities and Groups in Bifurcation Theory. 1988;Springer-Verlag, New York.
53. Gaeta G. Bifurcation and symmetry breaking. Phys. Rep. 189:1990;1-87.
54. Chossat P., Koenig M. Characterization of bifurcations for vector fields which are equivariant under the action of a compact Lie group. C. R. Acad. Sci. (Paris). 318:1994;31-36.
55. Field M. Equivariant dynamical systems. Bull. Amer. Math. Soc. 76:1970;1314-1318.
56. Ruelle D. Bifurcations in the presence of a symmetry group. Arch. Rat. Mech. Anal. 51:1973;136-152.
57. Sattinger D. H. Group Theoretic Methods in Bifurcation Theory. Lect. Notes Math. 762:1979;Springer-Verlag, New York/Berlin.
58. Sattinger D. H. Branching in the Presence of Symmetry. SIAM. 1984.
59. Olver P. J. Applications of Lie Groups to Differential Equations. 1986;Springer-Verlag, Berlin.
60. Bluman G. W., Kumei S. Symmetries and Differential Equations. 1989;Springer-Verlag, Berlin.
61. Stephani H. Differential Equations. Their Solution using Symmetry. 1991;Cambridge Univ. Press, Cambridge.
62. Gaeta G. Nonlinear Symmetry and Nonlinear Equations. 1994;Kluwer, Dordrecht.
63. Olver P. J. Equivariants, Invariants, and Symmetry. 1995;Cambridge Univ Press, Cambridge.
64. G. Gaeta, P. Morando, 1996, Commuting-flow symmetries and common solutions to differential equations with common symmetry.
65. Palais R. S. The principle of symmetric criticality. Comm. Math. Phys. 69:1979;19-30.
66. R. S. Palais, 1984, Applications of the symmetric criticality principle in mathematical physics and differential geometry, Proceedings, 1981 Shanghai Symposium on Differential Geometry and Differential Equations, Gu, Chaohao, Science Press, Beijing.
67. Ambrosetti A. Critical Points and Nonlinear Variational Problems. Mem. Soc. Math. France. 49:1992.
68. Palais R. S. Morse theory on Hilbert manifolds. Topology. 2:1963;299-340.
69. Goresky M., MacPherson R. Stratified Morse theory. 1988;Springer-Verlag, New York/Berlin.
70. Gaeta G. Counting symmetry breaking solutions to symmetric variational problems. Int. J. Theor. Phys. 35:1996;217-229.
71. Michel L. Extrema des fonctions sur la zone de Brillouin, invariantes par le groupe de symétrie du cristal et le renversement du temps. C. R. Acad. Sci. Paris. B-322:1996;223-230.
72. Cabibbo N., Maiani L. Weak interactions and the breaking of hadronic symmetry. Conversi M. Evolution of particle Physics (E. Amaldi Festschrift). 1970;50-80 Academic Press, New York/London.
73. S. Klimek, W. Kondracki, W. Oledzki, P. Sadowski, 1988, The density problem for infinite dimensional group actions, 68, 3, 10.
74. Babelon O., Viallet C. M. The riemannian geometry of the configuration space of gauge theories. Comm. Math. Phys. 81:1981;515-525.
75. P. Cotta-Ramusino, C. Reina, 1984, The action of the group of bundle automorphisms on the space of connections and the geometry of gauge theories, 1, 121, 155.
76. Abbati M. C., Cirelli R., Manià A. The orbit space of the action of gauge transformation group on connections. J. Geom. Phys. 6:1989;537-558.
77. M. C. Abbati, R. Cirelli, A. Manià, P. Michor, 1989, The Lie group of automorphisms of a principal bundle, 6, 215, 235.
78. Duistermaat J. J., Heckman G. J. On the variation in the cohomology in the symplectic form of the reduced phase space. Invent. Math. 69:1982;259.
79. Bismut J. M. Localization formulas, superconnections, and the index theorem for families. Comm. Math. Phys. 103:1986;127.
80. Jeffrey L. C., Kirwan F. C. Localization and the quantization conjecture. Topology. 36:1997;647-694.
81. Ehresman C. Les prolongements d'une variété différentiable, I-V. C. R. Acad. Sci. (Paris). 233:1951.
82. Koszul J. L. Lectures on Fibre Bundles and Differential Geometry (Tata Institute). 1986;Springer-Verlag, New York/Berlin.