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ON THE HAMILTONIAN FORM OF THE EINSTEIN EQUATIONS FOR GRAVITATIONAL FIELD

B. A. FAYZULLAEV

Theoretical Physics Department, National University of Uzbekistan, Tashkent 700095, Uzbekistan

https://doi.org/10.1142/S0217751X10049840Cited by:1 (Source: Crossref)

Abstract

It is shown that the Einstein gravitational equations and the canonical equations, which follow from the Dirac–Schwinger Hamiltonian, in the Faddeev variables coincide. To prove this, first, the Einstein equations are rewritten in canonical variables and then the time derivative of the generalized momenta of the gravitational field in Faddeev form are calculated using canonical Poisson brackets. The results coincide.

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References

P. A. M. Dirac, Proc. R. Soc. A 246, 333 (1958), DOI: 10.1098/rspa.1958.0142. Crossref, ADS, Google Scholar
J. Schwinger, Phys. Rev. 130, 1253 (1963), DOI: 10.1103/PhysRev.130.1253. Crossref, Web of Science, ADS, Google Scholar
L. D. Faddeev, Sov. Phys. Usp. 25, 130 (1982), DOI: 10.1070/PU1982v025n03ABEH004517. Crossref, Web of Science, ADS, Google Scholar
R. Arnowitt, S. Deser and C. W. Misner, Gravitation: An Introduction to Current Research, ed. L. Witten (Wiley, 1962) pp. 227–264, arXiv:gr-qc/0405109. Google Scholar
R. N. Ghalati, A novel Hamilton formulation of first order Einstein–Hilbert action: Connection with ADM, diffeomorphism invariance and linearized theory, , arXiv:0901.3344 . Google Scholar
N. Kiriushcheva and S. V. Kuzmin, The Hamiltonian formulation of general relativity: Myths and reality , arXiv:0809.0097 . Google Scholar
N. Kiriushchevaet al., Phys. Lett. A 372, 5101 (2008), arXiv:0808.2623 DOI: 10.1016/j.physleta.2008.05.081. Crossref, Web of Science, ADS, Google Scholar
T. P. Shestakova, Hamilton formulation of general relativity 50 years after the Dirac celebrated paper: Do unsolved problems still exist? , arXiv:0911.5252 . Google Scholar
A. Anderson and J. W. York, Phys. Rev. Lett. 81, 1151 (1998), arXiv:gr-qc/9807041. Google Scholar
P. A. M. Dirac , Lectures on Quantum Mechanics ( Yeshiva University , 1964 ) . Google Scholar
M. Henneaux and C. Teitelboim , Quantization of Gauge Systems ( Princeton University Press , 1994 ) . Google Scholar
L. V. Prokhorov and S. V. Shabanov , Hamiltonian Mechanics of Gauge Systems ( St. Petersbourg University Press , 1997 ) . Google Scholar