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TMF, 2006, Volume 148, Number 3, Pages 459–494 (Mi tmf2327)  

This article is cited in 4 scientific papers (total in 4 papers)

Polynomial Hamiltonian form of general relativity

M. O. Katanaev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The phase space of general relativity is extended to a Poisson manifold by inclusion of the determinant of the metric and conjugate momentum as additional independent variables. As a result, the action and the constraints take a polynomial form. We propose a new expression for the generating functional for the Green's functions. We show that the Dirac bracket defines a degenerate Poisson structure on a manifold and the second-class constraints are the Casimir functions with respect to this structure. As an application of the new variables, we consider the Friedmann universe.

Keywords: general relativity, Hamiltonian formalism

DOI: https://doi.org/10.4213/tmf2327

Full text: PDF file (550 kB)
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English version:
Theoretical and Mathematical Physics, 2006, 148:3, 1264–1294

Bibliographic databases:

Document Type: Article
Received: 27.10.2005
Revised: 27.02.2006

Citation: M. O. Katanaev, “Polynomial Hamiltonian form of general relativity”, TMF, 148:3 (2006), 459–494; Theoret. and Math. Phys., 148:3 (2006), 1264–1294

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Dodin I.Y., Fisch N.J., “Vlasov equation and collisionless hydrodynamics adapted to curved spacetime”, Phys. Plasmas, 17:11 (2010), 112118  crossref  adsnasa  isi  scopus  scopus
    2. Kiriushcheva N., Kuzmin S.V., “The Hamiltonian of Einstein affine-metric formulation of General Relativity”, Eur. Phys. J. C Part Fields, 70:1-2 (2010), 389–422  crossref  adsnasa  isi  scopus  scopus
    3. Derezin S., “Gauss–Codazzi Equations for Thin Films and Nanotubes Containing Defects”, Shell-Like Structures: Non-Classical Theories and Applications, Advanced Structured Materials, 15, ed. Altenbach H. Eremeyev V., Springer-Verlag Berlin, 2011, 531–548  crossref  isi  elib
    4. Gielen S., Ardon Rodrigo de Leon, Percacci R., “Gravity With More Or Less Gauging”, Class. Quantum Gravity, 35:19 (2018), 195009  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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