Eur. Phys. J. Plus (2019) 134: 152
https://doi.org/10.1140/epjp/i2019-12601-7

Regular Article

Canonical and symplectic analysis of actions describing linearized gravity

¹ Instituto de Física Luis Rivera Terrazas, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48 72570, Puebla Pue., Mexico
² Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado postal 1152, 72001, Puebla, Pue., Mexico

^* e-mail: aescalan@ifuap.buap.mx

Received: 22 November 2017
Accepted: 28 February 2019
Published online: 15 April 2019

Abstract

By using the canonical and symplectic approaches an (nonstandard) alternative action describing linearized gravity is studied. We identify the complete set of Dirac's constraints, the counting of physical degrees of freedom is performed and the Dirac brackets are constructed. Furthermore, the symplectic analysis is developed which includes the complete set of Faddeev-Jackiw constraints and a symplectic tensor; from that symplectic matrix we show that the generalized Faddeev-Jackiw brackets and the Dirac ones coincide to each other. With all these results at hand, we prove that the number of physical degrees of freedom are eight, thus, we conclude that the theory does not describe the dynamics of linearized gravity. In addition, we also develop the symplectic analysis of standard linearized gravity and we compare the results for both standard and nonstandard theories. Finally we present some remarks and conclusions.