A proposed proper EPRL vertex amplitude

Details A proposed proper EPRL vertex amplitude A proposed proper EPRL vertex amplitude

2011-11-11

arxiv.org/abs/1111.2865v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages. Review material abbreviated, section 2 better organized, and typos corrected

Scientific paper

As established in a prior work of the author, the linear simplicity constraints used in the construction of the so-called `new' spin-foam models mix three of the five sectors of Plebanski theory, only one of which is gravity in the usual sense, and this is the reason for certain `unwanted' terms in the asymptotics of the EPRL vertex amplitude as calculated by Barrett et al. In the present paper, an explicit classical discrete condition is derived that isolates the desired gravitational sector, which we call (II+), following other authors. This condition is quantized and used to modify the vertex amplitude, yielding what we call the `proper EPRL vertex amplitude.' This vertex still depends only on standard SU(2) spin-network data on the boundary, is SU(2) gauge invariant, and is linear in the boundary state, as required. In addition, the asymptotics now consist in the single desired term of the form $e^{iS_{\Regge}}$, and all degenerate configurations are exponentially suppressed.

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