Abstract
A geometrization of the Yang-Mills field, by which an SU(2) gauge theorybecomes equivalent to a 3-space geometry—or optical system—is examined. Ina first step, ambient space remains Euclidean and current problems on flat spacecan be looked at from a new point of view. The Wu-Yang ambiguity, for example,appears related to the multiple possible torsions of distinct metric-preservingconnections. In a second step, the ambient space also becomes curved. In thegeneric case, the strictly Riemannian metric sector plays the role of an arbitraryhost space, with the gauge potential represented by a contorsion. For some fieldconfigurations, however, it is possible to obtain a purely metric representation.In those cases, if the space is symmetric homogeneous, the Christoffel connectionsare automatically solutions of the Yang-Mills equations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Aldrovandi, R., and Pereira, J. G. (1995). An Introduction to Geometrical Physics, World Scientific, Singapore.
Arnold, V. I. (1978). Mathematical Methods of Classical Mechanics, Springer, New York, Appendix.
Calvo, M. (1977). Phys. Rev. D 15, 1733.
Chandrasekhar, S. (1992). The Mathematical Theory of Black Holes, Oxford University Press.
Doria, F. A. (1981). Commun. Math. Phys. 79, 435.
Drechsler, W., and Rosenblum, A. (1981). Phys. Lett. 106B, 81.
Faddeev, L. D., and Slavnov, A. A. (1978). Gauge Fields. Introduction to Quantum Theory, Benjamin/Cummings, Reading, Massachusetts.
Feynman, R. P. (1977). In Weak and Electromagnetic Interactions at High Energy, North-Holland, Amsterdam, ff. pp. 191.
Freedman, D. Z., and Khuri, R. R. (1994). Phys. Lett. B 329, 263.
Freedman, D. Z., Haagensen, P. E., Johnson, K., and Latorre, J. I. (1993). MIT preprint CTP 2238.
Greub, W. H., Halperin, S., and Vanstone, R. (1972). Connections, Curvature and Cohomology, Volume II: Lie Groups, Principal Bundles and Characteristic Classes, Academic Press, New York, p. 344.
Guillemin, V., and Sternberg, S. (1977). Geometric Asymptotics, AMS, Providence, Rhode Island.
Haagensen, P. E. (1993). Lecture at the XIII Particles and Nuclei International Conference, Peruggia, Italy, June¶July 1993; Barcelona preprint UB-ECM-PF 93/16.
Harnad, J., Tafel, J., and Shnider, S. (1980). J. Math. Phys. 21, 2236.
Hawking, S.W., and Ellis, G. F. R. (1973). The Large Scale Structure of Space-Time, Cambridge University Press.
Itzykson, C., and Zuber, J.-B. (1980). Quantum Field Theory, McGraw-Hill, New York.
Jackiw, R. (1980). Rev. Mod. Phys. 52, 661.
Johnson, K. (1992). In QCD·20 Years Later, Aachen.
Kobayashi, S., and Nomizu, K. (1963). Foundations of Differential Geometry, Vol. 1, Interscience, New York.
Luneburg, R. K., (1966). Mathematical Theory of Optics, University of California Press, Berkeley.
Lunev, F. A. (1992). Phys. Lett. B 295, 99.
Mostow, M. A. (1980). Commun. Math. Phys. 78, 137.
Nowakowski, J., and Trautman, A. (1978). J. Math. Phys. 19, 1100.
Ramond, P. (1981). Field Theory: A Modern Primer, Benjamin/Cummings, Reading, Massachusetts.
Roskies, R. (1977). Phys. Rev. D 15, 1731.
Weinberg, S. (1972). Gravitation and Cosmology, Wiley, New York, esp. Chapter XIII.
Wong, S. K. (1970). Nuovo Cimento 65A, 689.
Wu, T. T., and Yang, C. N. (1975). Phys. Rev. D 12, 3843, 3845.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Aldrovandi, R., Barbosa, A.L. Yang-Mills Fields as Optical Media. International Journal of Theoretical Physics 39, 1085–1099 (2000). https://doi.org/10.1023/A:1003658625955
Issue Date:
DOI: https://doi.org/10.1023/A:1003658625955