FADDEEV GRAVITY ACTION ON THE PIECEWISE CONSTANT FUNDAMENTAL VECTOR FIELDS
In the Faddeev formulation of gravity, the metric is regarded as composite field, bilinear of d = 10 4-vector fields. We derive the minisuperspace (discrete) Faddeev action by evaluating the Faddeev action on the spacetime composed of the (flat) 4-simplices with constant 4-vector fields. This is an analog of the Regge action obtained by evaluating the Hilbert-Einstein action on the spacetime composed of the flat 4-simplices. One of the new features of this formulation is that the simplices are not required to coincide on their common faces. Also an analog of the Barbero-Immirzi parameter γ can be introduced in this formalism.
Keywords: Einstein gravity, Regge calculus, composite metric, Faddeev gravity, discrete gravity
References:
[1] Regge T. 1961 Nuovo Cimento 19 558.
[2] Regge T. and Williams R. M. 2000 Journ. Math. Phys. 41 3964 [arXiv:0012035 [gr-qc]].
[3] Hamber H. W. 2009 Gen. Rel. Grav. 41 817 [arXiv:0901.0964 [gr-qc]].
[4] Ambjorn J., Goerlich A., Jurkiewicz J., and Loll R. 2012 Phys. Rep. 519 127 [arXiv:1203.3591 [hep-th]].
[5] Faddeev L. D. 2011 Theor. Math. Phys. 166 279.
[6] Khatsymovsky V. M. 2013 Class. Quant. Grav. 30 095006 [arXiv:1201.0806 [gr-qc]].
[7] Barbero J. F. 1995 Phys. Rev. D 51 5507 [arXiv:9410014 [gr-qc]].
[8] Holst S. 1996 Phys. Rev. D 53 5966 [arXiv:9511026 [gr-qc]].
[9] Immirzi G. 1997 Nucl. Phys. Proc. Suppl. 57 65 [arXiv:9701052 [gr-qc]].
[10] Fatibene L., Francaviglia M., and Rovelli C. 2007 Class. Quantum Grav. 24 4207 [arXiv:0706.1899 [gr-qc]].
[11] Khatsymovsky V. M. 2014 Mod. Phys. Lett. A 29 1450141 [arXiv:1408.6375 [gr-qc]].
[12] Feinberg G., Friedberg R., Lee T. D., and Ren M. C. 1984 Nucl. Phys. B 245 343.
[13] Ashtekar A., Rovelli C. and Smolin L. 1992 Phys. Rev. Lett. 69 237 [arXiv:9203079 [hep-th]].
[14] Loll R. 1997 Class. Quant. Grav. 14 1725 [arXiv:9612068 [gr-qc]].
[15] Ashtekar A., Baez J., Corichi A., and Krasnov K. 1998 Phys. Rev. Lett. 80 904 [arXiv:9710007 [gr-qc]].
( 548.15 kB ) 
( 436.96 kB )
Issue: 12, 2014
Series of issue: Issue 12
Pages: 131 — 134
Downloads: 301