Abstract
We perform, in a manifestly \(\mathrm{SO}(n-1,1)\) [\(\mathrm{SO}(n)\)] covariant fashion, the Hamiltonian analysis of general relativity in n dimensions written as a constrained BF theory. We solve the constraint on the B field in a way naturally adapted to the foliation of the spacetime that avoids explicitly the introduction of the vielbein. This leads to a form of the action involving a presymplectic structure, which is reduced by doing a suitable parametrization of the connection and then, after integrating out some auxiliary fields, the Hamiltonian form involving only first-class constraints is obtained.
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Acknowledgements
We thank Diego Gonzalez for useful comments and suggestions on a preliminary version of this manuscript. This work was partially supported by Fondo SEP-Cinvestav and by Consejo Nacional de Ciencia y Tecnología (CONACyT), México, Grant No. A1-S-7701. M. C. gratefully acknowledges the support of a DGAPA-UNAM postdoctoral fellowship.
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Montesinos, M., Escobedo, R. & Celada, M. Straightforward Hamiltonian analysis of BF gravity in n dimensions. Gen Relativ Gravit 53, 52 (2021). https://doi.org/10.1007/s10714-021-02821-3
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DOI: https://doi.org/10.1007/s10714-021-02821-3