Geometrical properties of gauge theories. (English) Zbl 0611.53078
The authors calculate the metric of the orbit space in the free Yang- Mills theory and in scalar electrodynamics. From this metric they derive the curvature of the orbit space and examine singular points where the curvature is ill defined. Finally relation of the metric to the topological properties of the orbit space and the instanton solution is discussed.
Reviewer: M.Martellini
MSC:
| 53C80 | Applications of global differential geometry to the sciences |
| 81T08 | Constructive quantum field theory |
| 81V10 | Electromagnetic interaction; quantum electrodynamics |
References:
| [1] | Yang, C. N.; Mills, R. L., Phys. Rev., 96, 161 (1954) |
| [2] | Weinberg, S., Phys. Rev. Lett., 19, 1264 (1964) |
| [3] | Atiyah, M. F.; Jones, J. D.S., Comm. Math. Phys., 61, 97 (1978) · Zbl 0387.55009 |
| [4] | Singer, I. M., Phys. Scripta, 24, 817 (1981) · Zbl 1063.81623 |
| [5] | Babelon, O.; Viallet, C. M., Comm. Math. Phys., 81, 515 (1981) · Zbl 0495.58003 |
| [6] | Narasimhan, M. S.; Ramadas, S., Comm. Math. Phys., 67, 21 (1979) |
| [7] | Asorey, M.; Mitter, P. K., Comm. Math. Phys., 80, 43 (1981) · Zbl 0476.58008 |
| [8] | Mitter, P. K.; Viallet, C. M., Comm. Math. Phys., 79, 457 (1981) · Zbl 0474.58004 |
| [9] | Lee, T. D., (Particle Physics and Introduction into Field Theory (1981), Harwood Academic Pub: Harwood Academic Pub New York), 415 |
| [10] | Creutz, M.; Muzinich, I. J.; Tudron, T. N., Phys. Rev. D, 19, 531 (1979) |
| [11] | Callan, C. G.; Dashen, R. F.; Gross, D. J., Phys. Lett. B, 63, 334 (1976) |
| [12] | Belavin, A. A.; Polyakov, A. M.; Schwartz, A. S.; Tyupkin, Yu. S., Phys. Lett. B, 59, 85 (1975) |
| [13] | Huang, K., (Quarks, Leptons and Gauge Fields (1982), World Scientific: World Scientific Singapore), 168 |
| [14] | McLaughlin, D., J. Math. Phys., 13, 1099 (1972) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
