Abstract
Starting from a knowledge of certain identities in the Lagrangian description, the diffeomorphism transformations of metric and connection are obtained for both the second order (metric) and the first order (Palatini) formulations of gravity. These transformations are found to be identical to the diffeomorphism transformations of the fields which establish a one-to-one mapping between the gauge and diffeomorphism symmetry.
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References
Carroll, S.M.: An Introduction to General Relativity: Space time and Geometry. Addison Wesley, Reading (2003)
Einstein, A., Straus, E.G.: A generalization of the relativistic theory of gravitation, 2. Ann. Math. 47, 731 (1946)
Einstein, A., Kaufman, B.: A new form of the general relativistic field equations. Ann. Math. 62, 128 (1955)
Palatini, A.: Deduzione invariantiva delle equazioni gravitazionali dal. principio di Hamilton. Rend. Circ. Mat. Palermo 43, 203 (1919)
Deser, S., Zumino, B.: Consistent supergravity. Phys. Lett. B 62, 335 (1976)
M Dirac, P.A.: Lectures on Quantum Mechanics. Yeshiva University Press, New York (1964)
Castellani, L.: Symmetries in constrained Hamiltonian systems. Ann. Phys. 143, 357–371 (1982)
Mukherjee, P., Saha, A.: Gauge invariances vis-a-vis diffeomorphisms in second order metric gravity. arXiv:0705.4358 [hep-th]
Arnowitt, R., Deser, S., Misner, C.W.: Gravitation: an Introduction to Current Research. Wiley, New York (1962). L. Witten (ed.)
Gitman, D.M., Tyutin, I.V.: Quantization of Fields with Constraints. Springer, Berlin (1990)
Shirzad, A.: Gauge symmetry in Lagrangian formulation and Schwinger models. J. Phys. A 31, 2747–2760 (1998)
Banerjee, R., Rothe, H.J., Rothe, K.D.: Master equation for Lagrangian gauge symmetries. Phys. Lett. B 479, 429–434 (2000)
Banerjee, R., Rothe, H.J., Rothe, K.D.: Recursive construction of generator for Lagrangian gauge symmetries. J. Phys. A 33, 2059–2068 (2000). hep-th/9909039
Banerjee, R., Samanta, S.: Gauge generators, transformations and identities on a noncommutative space. Eur. Phys. J. C 51, 207–215 (2007). hep-th/0608214
Weinberg, S.: Gravitation and Cosmology. Wiley, New York (1972)
Ortin, T.: Gravity and Strings. Cambridge University Press, Cambridge (2004)
Gegenberg, J., Kelly, P.F., Mann, R.B., Vincent, D.: Theories of gravitation in two dimensions. Phys. Rev. D 37, 3463 (1988)
Mukhopadhyay, A., Padmanabhan, T.: Holography of gravitational action functionals. Phys. Rev. D 74, 124023 (2006). hep-th/0608120
Exirifard, Q., Sheikh-Jabbari, M.M.: Lovelock gravity at the crossroads of Palatini and metric formulations. arXiv:0705.1879 [hep-th]
Carroll, S.M., Duvvuri, V., Trodden, M., Turner, M.S.: Is cosmic speed-up due to new gravitational physics? Phys. Rev. D 70, 043528 (2004). astro-ph/0306438
Vollick, D.N.: 1/R Curvature corrections as the source of the cosmological acceleration. Phys. Rev. D 68, 063510 (2003). astro-ph/0306630
Nojiri, S., Odintsov, S.D.: Modified gravity with negative and positive powers of the curvature: Unification of the inflation and of the cosmic acceleration. Phys. Rev. D 68, 123512 (2003). hep-th/0307288
Vollick, D.N.: On the viability of the Palatini form of 1/R gravity. Class. Quantum Gravity 21, 3813–3816 (2004). gr-qc/0312041
Flanagan, E.E.: Higher order gravity theories and scalar tensor theories. Class. Quantum Gravity 21, 417–426 (2003). gr-qc/0309015
Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields, 4th edn. Pergamon, Elmsford (1994)
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Samanta, S. Diffeomorphism Symmetry in the Lagrangian Formulation of Gravity. Int J Theor Phys 48, 1436–1448 (2009). https://doi.org/10.1007/s10773-008-9914-8
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DOI: https://doi.org/10.1007/s10773-008-9914-8