Cosmological Einstein-Yang-Mills equations

Journal of Mathematical Physics

Volumn 38, Issue 9, 1997, Pages 4696-4713

  Darian, B K ^a   Kunzle H P ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039970339     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532116     Document Type: Article

References (21)

1. L. H. Ford, "Inflation driven by a vector field." Phys. Rev. D 40, 967-972 (1989).
2. H. C. Wang, "On invariant connections over a principal bundle," Nagoya Math. J. 13, 1-19 (1958).
3. P. V. Moniz and J. M. Mourão, "Homogeneous and isotropic closed cosmologies with a gauge sector," Class. Quantum Grav. 8, 1815-1831 (1991); O. Bertolami, J. M. Mourão, R. F. Picken, and I. P. Volobujev, "Dynamics of Euclideanized Einstein-Yang-Mills systems with arbitrary gauge groups," Int. J. Mod. Phys. A 6, 4149-4180 (1991).
4. P. V. Moniz and J. M. Mourão, "Homogeneous and isotropic closed cosmologies with a gauge sector," Class. Quantum Grav. 8, 1815-1831 (1991); O. Bertolami, J. M. Mourão, R. F. Picken, and I. P. Volobujev, "Dynamics of Euclideanized Einstein-Yang-Mills systems with arbitrary gauge groups," Int. J. Mod. Phys. A 6, 4149-4180 (1991).
5. P. V. Moniz, J. M. Mourão, and P. M. Sá, "The dynamics of flat Friedmann-Robertson-Walker inflationary model in the presence of gauge fields," Class. Quantum Grav. 10, 517-534 (1993).
6. D. Kapetanakis, G. Koutsoumbas, A. Lukas, and P. Mayr, "Quantum cosmology with Yang-Mills fields," Nucl. Phys. B 433, 435-466 (1995).
7. D. V. Gal'tsov and M. S. Volkov, "Yang-Mills cosmology. Cold matter for a hot universe," Phys. Lett. B 256, 17-21 (1991).
8. Y. Hosotani, "Exact solution to the Einstein-Yang-Mills equations," Phys. Lett. B 147, 44-46 (1984).
9. B. K. Darian and H. P. Künzle, "Axially symmetric Bianchi I Yang-Mills cosmology as a dynamical system," Class. Quantum Grav. 12, 2651-2662 (1996).
10. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry II (Interscience Wiley, New York, 1969).
11. J. Harnad, S. Shnider, and L. Vinet, "Group actions on principal bundles and invariance conditions for gauge fields," J. Math. Phys. 21, 2719-2724 (1980).
12. A. Jadczyk, "Symmetry of Einstein-Yang-Mills systems and dimensional reduction," J. Geom. Phys. 1, 97-126 (1984).
13. E. B. Dynkin, "Semisimple subalgebras of semisimple Lie algebras," Am. Math. Soc. Transl. 6, 111-244 (1957).
14. E. Dynkin, "Maximal subgroups of the classical groups," Am. Math. Soc. Transl. 6, 245-378 (1957).
15. H. P. Künzle, "SU(n)-Einstein-Yang-Mills fields with spherical symmetry," Class. Quantum Grav. 8, 2283-2297 (1991).
16. Perhaps one should take SO(3) rather than SU(2) as the isotropy group. But it is clear that a covering group of an isometry group of a Riemannian manifold M will also act in a well-defined way via projections, at least if M is also simply connected. We will not consider these topological questions here.
17. W. Fulton and J. Harris, Representation Theory: A First Course (Springer, Berlin, 1991).
18. D. Kramer, H. Stephani, M. MacCallum, and E. Herlt, "Exact solutions of Einstein's field equations," VEB Deutscher Verlag der Wissenschaften, 1980.
19. J. Patera and P. Winternitz, "Subalgebras of real three-and four-dimensional Lie algebras," J. Math. Phys. 18, 1449-1455 (1977).
20. M. Tanimoto, T. Koike, and A. Hosoya, "Dynamics of compact homogeneous universes," J. Math. Phys. 38, 350-368 (1996).
21. O. Brodbeck and N. Straumann, "A generalized Birkhoff theorem for the Einstein-Yang-Mills system," J. Math. Phys. 34, 2412-2423 (1993).