Analysis of Hamiltonian formulations of linearized General Relativity

TL;DR

This paper compares different Hamiltonian formulations of linearized General Relativity, showing their similarities, differences, and the canonical transformations linking them, with implications for the full theory.

Contribution

It demonstrates that various Hamiltonian formulations of linearized GR are related by explicit canonical transformations and clarifies their differences and similarities.

Findings

Hamiltonians differ but share the same gauge invariance

Formulations are connected by explicit canonical transformations

Unnecessary to modify covariant Lagrangian in linear models

Abstract

The different forms of the Hamiltonian formulations of linearized General Relativity/spin-two theories are discussed in order to show their similarities and differences. It is demonstrated that in the linear model, non-covariant modifications to the initial covariant Lagrangian (similar to those modifications used in full gravity) are in fact unnecessary. The Hamiltonians and the constraints are different in these two formulations but the structure of the constraint algebra and the gauge invariance derived from it are the same. It is shown that these equivalent Hamiltonian formulations are related to each other by a canonical transformation which is explicitly given. The relevance of these results to the full theory of General Relativity is briefly discussed.