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Remarks on the linking theory of shape dynamics

Westminster College, 501 Westminster Ave., Fulton, Missouri 65251, USA

https://doi.org/10.1142/S0219887818500986Cited by:0 (Source: Crossref)

Abstract

This short note is an attempt to bring out the geometric structures in the linking theory of shape dynamics. Symplectic induction is applied to give a natural construction of the extended phase space used in the linking theory as a trivial vector bundle over the original phase space for canonical gravity. The geometry of the gauge fixing for shape dynamics is analyzed with the assistance of the Lichnerowicz–York equation lifted to the extended phase space. An alternative description is provided to show how the same geometry simply derives from symplectic induction.

Keywords:

AMSC: 53D83

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