Canonical and Symplectic analysis of actions describing linearized gravity

TL;DR

This paper applies canonical and symplectic methods to analyze a nonstandard action for linearized gravity, revealing it does not describe the expected gravitational degrees of freedom and comparing it with the standard theory.

Contribution

It provides a detailed canonical and symplectic analysis of a nonstandard linearized gravity action, showing it lacks the correct physical degrees of freedom.

Findings

The nonstandard action has eight physical degrees of freedom.

Symplectic and Dirac brackets coincide in this analysis.

The nonstandard theory does not describe linearized gravity dynamics.

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.