Analysis of Hamiltonian formulations of linearized General Relativity

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.

Section Discussion is modified and references are added; 19 pages

References in corpus (10)

• Lorentz violation in the linearized gravity
• The Hamiltonian formulation of General Relativity: myths and reality
• Diffeomorphism Invariance in the Hamiltonian formulation of General Relativity
• Gauge invariances vis-{á}-vis Diffeomorphisms in second order metric gravity: A new Hamiltonian approach
• Gauge Symmetry and Consistent Spin-Two Theories
• Symmetries of topological gravity with torsion in the hamiltonian and lagrangian formalisms
• The Hamiltonian of Einstein affine-metric formulation of General Relativity
• Diffeomorphism Symmetry in the Lagrangian Formulation of Gravity
• Two-dimensional metric and tetrad gravities as constrained second order systems
• Hamiltonian reduction of spin-two theory and of solvable cosmologies

Cited by in corpus (7)

• The weak field limit of quantum matter back-reacting on classical spacetime
• A connection between linearized Gauss-Bonnet gravity and classical electrodynamics
• Canonical Noether and the energy-momentum non-uniqueness problem in linearized gravity
• On the breakdown of space-time in general relativity
• On the Quantization of the Higher Spin Fields
• The Canonical Structure of the First Order Einstein-Hilbert Action with a Flat Background
• Abelian Ashtekar formulation from the ADM action