1304.5627 (Muxin Han)

On Spinfoam Model in Large Spin Regime    [PDF]

Muxin Han

We study the semiclassical behavior of Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model, by taking into account of the sum over spins in the large spin regime. We also employ the method of stationary phase analysis with parameters and the so called, almost-analytic machinery, in order to find the asymptotic behaviour of the contributions from all possible large spin configurations in the spinfoam model. The spins contributing the sum is written as J_f=\lambda j_f where \lambda is a large parameter, which resulting in an asymptotic expansion via stationary phase approximation. The analysis shows that at least for the simplicial Lorentzian geometries (as spinfoam critical configurations), they contribute the leading order approximation of spinfoam amplitude only when their deficit angles satisfy \gamma\Theta_f<<\lambda^{-1/2} mod 4\pi Z, when one treats the Barbero-Immirzi parameter \gamma o(1). We also discuss the consequences of such a result.

View original: http://arxiv.org/abs/1304.5627