Generalizations of the Pontryagin and Husain-Kuchař actions to manifolds with boundary
J. Barbero G. (Instituto de Estructura de la Materia, CSIC, Serrano 123, Madrid, 28006, Spain, Grupo de Teorías de Campos y Física Estadística, Instituto Gregorio Millán (UC3M), Unidad Asociada al Instituto de Estructura de la Materia, CSIC, Madrid, Spain); Bogar Díaz (Instituto de Estructura de la Materia, CSIC, Serrano 123, Madrid, 28006, Spain); Juan Margalef-Bentabol (Institute for Gravitation and the Cosmos & Physics Department, Penn State, University Park, PA, 16802, U.S.A., Grupo de Teorías de Campos y Física Estadística, Instituto Gregorio Millán (UC3M), Unidad Asociada al Instituto de Estructura de la Materia, CSIC, Madrid, Spain, Laboratory of Geometry and Dynamical Systems, Department of Mathematics, EPSEB, Universitat Politécnica de Catalunya, BGSMath, Barcelona, Spain); Eduardo Villaseñor (Grupo de Teorías de Campos y Física Estadística, Instituto Gregorio Millán (UC3M), Unidad Asociada al Instituto de Estructura de la Materia, CSIC, Madrid, Spain, Universidad Carlos III de Madrid, Avda. de la Universidad 30, Leganés, 28911, Spain)
In this paper we study a family of generalizations of the Pontryagin and Husain-Kuchǎr actions on manifolds with boundary. In some cases, they describe well- known models — either at the boundary or in the bulk — such as 3-dimensional Euclidean general relativity with a cosmological constant or the Husain-Kuchǎr model. We will use Hamiltonian methods in order to disentangle the physical and dynamical content of the systems that we discuss here. This will be done by relying on a geometric implementation of the Dirac algorithm in the presence of boundaries recently proposed by the authors.
