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arXiv · 2009.06311

Symmetry restriction and its application to gravity

Wojciech Kamiński·Klaus Liegener
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Abstract

In the Hamiltonian formulation, it is not a priori clear whether a symmetric configuration will keep its symmetry during evolution. In this paper, we give precise requirements of when this is the case and propose a symmetry restriction to the phase space of the symmetric variables. This can often ease computation, especially when transcending from the infinite dimensional phase space of a field theory to a possibly finite dimensional subspace. We will demonstrate this in the case of gravity. A prominent example is the restriction of full Hamiltonian general relativity to the cosmological configurations of Robertson-Walker type. We will demonstrate our procedure in this setting and extend it to examples which appear useful in certain approaches to quantum gravity.

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Wojciech Kamiński, Klaus Liegener. 2020-09-14. Symmetry restriction and its application to gravity. https://doi.org/10.1088/1361-6382%2Fabdf29

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