Faddeev-Jackiw quantization of spin-2 field

TL;DR

This paper applies the Faddeev-Jackiw method to analyze the Hamiltonian structure of the massless spin-2 field, revealing that not all non-propagating components can be gauge-fixed, with implications for understanding gravitational theories.

Contribution

It demonstrates the Hamiltonian analysis of the spin-2 field using the Faddeev-Jackiw method and shows the limitations of gauge fixing similar to electromagnetism.

Findings

Reduced Hamiltonian contains only traceless-transverse tensor

Not all non-propagating components are determined by constraints

No gauge choice can isolate only propagating modes

Abstract

We apply the Faddeev-Jackiw method to the Hamiltonian analysis of the massless spin-two field. As expected, the reduced Hamiltonian contains only the traceless-transverse tensor, while some, but not all of the non-propagating components are determined by the constraints of the theory. In particular, it is concluded that no gauge choice can be imposed on the fields such that only the propagating modes remain in the theory, meaning that for the spin-2 field there is no direct analogue to the Coulomb gauge of electromagnetism. Implications for General Relativity are discussed.