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ON SOME FEATURE AND APPLICATION OF THE FADDEEV FORMULATION OF GRAVITY // Tomsk State Pedagogical University Bulletin. 2012. Issue 13 (128). P. 76-80

In the Faddeev formulation of gravity, the metric is regarded as composite eld, bilinear of d = 10 4-vector fields. A unique feature is that this formulation admits the discontinuous elds. On the discrete level, when spacetime is decomposed into the elementary 4-simplices, this means that the 4-simplices may not coincide on their common faces, that is, be independent. We apply this to the particular problem of quantization of the surface regarded as that composed of virtually independent elementary pieces (2-simplices). We nd the area spectrum being proportional to the Barbero-Immirzi parameter y in the Faddeev gravity and described as a sum of spectra of separate areas. According to the known in the literature approach, we nd that exists ensuring Bekenstein-Hawking relation for the statistical black hole entropy for arbitrary d, in particular, y = 0:39... for genuine d = 10.

Keywords: Faddeev gravity, piecewise at spacetime, connection, area spectrum

FADDEEV GRAVITY ACTION ON THE PIECEWISE CONSTANT FUNDAMENTAL VECTOR FIELDS // Tomsk State Pedagogical University Bulletin. 2014. Issue 12 (153). P. 131-134

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