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arXiv · 2004.01650

Hamilton-Jacobi approach for Regge-Teitelboim cosmology

Alejandro Aguilar-Salas·Alberto Molgado·Efrain Rojas
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Abstract

The Hamilton-Jacobi formalism for a geodetic brane-like universe described by the Regge-Teitelboim model is developed. We focus on the description of the complete set of Hamiltonians that ensure the integrability of the model in addition to obtaining the Hamilton principal function $S$. In order to do this, we avoid the second-order in derivative nature of the model by appropriately defining a set of auxiliary variables that yields a first-order Lagrangian. Being a linear in acceleration theory, this scheme unavoidably needs an adequate redefinition of the so-called Generalized Poisson Bracket in order to achieve the right evolution in the reduced phase space. Further this Hamilton-Jacobi framework also enables us to explore the quantum behaviour under a semi-classical approximation of the model. A comparison with the Ostrogradski-Hamilton method for constrained systems is also provided in detail.

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Alejandro Aguilar-Salas, Alberto Molgado, Efrain Rojas. 2020-04-03. Hamilton-Jacobi approach for Regge-Teitelboim cosmology. https://doi.org/10.1088/1361-6382%2Fab87d9

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