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arXiv · 1112.2390

The geometric role of symmetry breaking in gravity

Derek K. Wise
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Abstract

In gravity, breaking symmetry from a group G to a group H plays the role of describing geometry in relation to the geometry the homogeneous space G/H. The deep reason for this is Cartan's "method of equivalence," giving, in particular, an exact correspondence between metrics and Cartan connections. I argue that broken symmetry is thus implicit in any gravity theory, for purely geometric reasons. As an application, I explain how this kind of thinking gives a new approach to Hamiltonian gravity in which an observer field spontaneously breaks Lorentz symmetry and gives a Cartan connection on space.

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Derek K. Wise. 2011-12-11. The geometric role of symmetry breaking in gravity. https://doi.org/10.1088/1742-6596/360/1/012017

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