Abstract
The Lie groups preserving degenerate quadratic forms appear in various contexts related to spacetime. The homogeneous Galilei group is the intersection of two such groups. The structure group of sub-Riemannian geometry and of singular semi-Riemannian geometry, as well as of some submanifolds of semi-Riemannian manifolds, is of this kind. Such groups are shown to replace the Lorentz group at a very large class of singularities in general relativity. Also, these groups are shown to be fundamental in Kaluza-Klein theory and in gauge theory, where they provide an explanation why we may not be able to probe extra-dimensional lengths.
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Stoica, O.C. (2016). Degenerate Metrics and Their Applications to Spacetime. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. LT 2015. Springer Proceedings in Mathematics & Statistics, vol 191. Springer, Singapore. https://doi.org/10.1007/978-981-10-2636-2_19
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DOI: https://doi.org/10.1007/978-981-10-2636-2_19
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