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Simplicity Constraints of Spinfoam Models
DING You * #
School of Science, Beijing Jiaotong University, Beijing 100044
*Correspondence author
#Submitted by
Subject:
Funding: Research Fund for the Doctoral Program of Higher Education of China （No.20120009120039）
Opened online:18 April 2017
Accepted by: none
Citation: DING You.Simplicity Constraints of Spinfoam Models[OL]. [18 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4724865
 
 
To give a mathematically rigorous path of obtaining Engle-Pereira-Rovelli-Livine spinfoam model, the implementation of simplicity constraints on the BF model is studied. In a simple way the boundary Hilbert space of the theory is defined; then it is shown directly that all constraints vanish on this space in a weak sense. It is pointed out that the general solution to this constraint (imposed weakly) depends on a quantum number in addition to those of loop quantum gravity. Finally, this construction is also generalized to Kami'nski-Kisielowski-Lewandowski version where the foam is not dual to a triangulation. It is shown that this theory can still be obtained as a constrained BF theory satisfying the simplicity constraint, now discretized on a general oriented 2-cell complex.
Keywords:Theoretical Physics; Loop Quantum Gravity; Spinfoam Models; simplicity constraints
 
 
 

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