This article is cited in 45 papers

Canonical formulation of the embedded theory of gravity equivalent to Einstein's general relativity

S. A. Paston, V. A. Franke

Saint-Petersburg State University

Abstract: We study the approach in which independent variables describing gravity are functions of the space–time embedding into a flat space of higher dimension. We formulate a canonical formalism for such a theory in a form that requires imposing additional constraints, which are a part of Einstein's equations. As a result, we obtain a theory with an eight-parameter gauge symmetry. This theory becomes equivalent to Einstein's general relativity either after partial gauge fixing or after rewriting the metric in the form that is invariant under the additional gauge transformations. We write the action for such a theory.

Keywords: isometric embedding, theory of gravity, canonical formalism.

Received: 20.12.2006

DOI: 10.4213/tmf6138

 English version: Theoretical and Mathematical Physics, 2007, 153:2, 1582–1596

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