Three roads to the geometric constraint formulation of gravitational theories with boundaries

J.F. Barbero G., M. Basquens, V. Varo, E.J. S. Villaseñor

Symmetry Vol. 13, nº. 8, pp. 1430-1 - 1430-23

Summary:

The Hamiltonian description of mechanical or field models defined by singular Lagrangians plays a central role in physics. A number of methods are known for this purpose, the most popular of them being the one developed by Dirac. Here, we discuss other approaches to this problem that rely on the direct use of the equations of motion (and the tangency requirements characteristic of the Gotay, Nester and Hinds method), or are formulated in the tangent bundle of the configuration space. Owing to its interesting relation with general relativity we use a concrete example as a test bed: an extension of the Pontryagin and Husain–Kuchař actions to four dimensional manifolds with boundary.

Keywords: geometric constraint algorithm; hamiltonian field theory; Husain–Kuchař model; pontryagin; three-dimensional general relativity; boundaries

JCR Impact Factor and WoS quartile: 2,940 - Q2 (2021); 2,200 - Q2 (2023)

DOI reference: https://doi.org/10.3390/sym13081430

Published on paper: August 2021.

Published on-line: August 2021.

Citation:
J.F. Barbero G., M. Basquens, V. Varo, E.J. S. Villaseñor, Three roads to the geometric constraint formulation of gravitational theories with boundaries. Symmetry. Vol. 13, nº. 8, pp. 1430-1 - 1430-23, August 2021. [Online: August 2021]