Asymptotic analysis of the EPRL four-simplex amplitude
John W. Barrett, R.J. Dowdall, Winston J. Fairbairn, Henrique Gomes,, Frank Hellmann
TL;DR
This paper analyzes the asymptotic behavior of the EPRL four-simplex amplitude in spin foam quantum gravity, showing it reproduces the Regge action in the semiclassical limit when boundary states represent non-degenerate geometries.
Contribution
It demonstrates the conditions under which the EPRL amplitude yields the Regge action, highlighting the importance of a canonical phase choice for boundary states.
Findings
The asymptotic formula contains the Regge action for non-degenerate geometries.
A specific phase choice for boundary states is necessary for correct semiclassical behavior.
The results connect spin foam models with classical general relativity in the semiclassical limit.
Abstract
The semiclassical limit of a 4-simplex amplitude for a spin foam quantum gravity model with an Immirzi parameter is studied. If the boundary state represents a non-degenerate 4-simplex geometry, the asymptotic formula contains the Regge action for general relativity. A canonical choice of phase for the boundary state is introduced and is shown to be necessary to obtain the results.
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