https://doi.org/10.1140/epjc/s10052-011-1678-2
Regular Article - Theoretical Physics
Analysis of the Hamiltonian formulations of linearized general relativity
1
Faculty of Science, University of Ontario Institute of Technology, L1H 7K4, Oshawa, Canada
2
Faculty of Arts and Social Science, Huron University College, N6G 1H3, London, Canada
3
Department of Applied Mathematics, University of Western Ontario, N6A 5B7, London, Canada
* e-mail: Kevin.Green@uoit.ca
Received:
29
April
2011
Published online:
17
June
2011
The different forms of the Hamiltonian formulations of linearized General Relativity/spin-2 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.
© Springer-Verlag / Società Italiana di Fisica, 2011
