Abstract
Using the invariant geometrical interpretation of gauge and Higgs fields, a simple derivation is given of the dimensional reduction procedure. The underlying assumption with regard to the Riemannian structure, group orbits and invariant connection are clarified and the critical points of the Higgs potential are shown to have a natural geometrical interpretation.
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References
Harnad, J., Shnider, S., and Vinet, L., J. Math. Phys. 20, 931 (1979).
Harnad, J., Shnider, S., and Vinet, L., ‘Group Actions on Principal Bundles and Invariance Conditions for Gauge Fields', preprint CRMA-899 (1979).
Forgacs, P., and Manton, N.S., ‘Space-Time Symmetries in Gauge Theories’, preprint LPTENS 79/3 (1979).
Kobayashi, S., and Nomizu, K., Foundations of Differential Geometry, Vol. I, Interscience, New York, 1963.
Cheeger, J., and Ebin, D. Comparison Theorems in Differential Geometry, North-Holland/American Elsevier (1975), Chap. 3.
Coleman, S., ‘Classical Lumps and Their Quantum Descendants’, Appendix A, Erice Lectures, 1975.
Harnad, J., Shnider, S., and Tafel, J., ‘Canonical Connections on Riemannian Symmetric Spaces and Solutions to the Einstein-Yang-Mills Equations’, preprint (CRMA-922 (1979).
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Harnad, J., Shnider, S. & Tafel, J. Group actions on principal bundles and dimensional reduction. Lett Math Phys 4, 107–113 (1980). https://doi.org/10.1007/BF00417502
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DOI: https://doi.org/10.1007/BF00417502