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Classical general relativity as BF-Plebanski theory with linear constraints

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons39400

Gielen,  Steffen
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons20698

Oriti,  Daniele
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1004.5371
(Preprint), 245KB

CQG_27_18_185017.pdf
(Any fulltext), 247KB

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Citation

Gielen, S., & Oriti, D. (2010). Classical general relativity as BF-Plebanski theory with linear constraints. Classical and quantum gravity, 27: 185017. doi:10.1088/0264-9381/27/18/085017.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-9DC5-C
Abstract
We investigate a formulation of continuum 4d gravity in terms of a constrained BF theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum gravity. We identify both the continuum version of the linear simplicity constraints used in the quantum discrete context and a linear version of the quadratic volume constraints that are necessary to complete the reduction from the topological theory to gravity. We illustrate and discuss also the discrete counterpart of the same continuum linear constraints. Moreover, we show under which additional conditions the discrete volume constraints follow from the simplicity constraints, thus playing the role of secondary constraints.