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arXiv · 2102.05881

Relating spin-foam to canonical loop quantum gravity by graphical calculus

Jinsong Yang·Cong Zhang·Yongge Ma
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Abstract

The graphical calculus method is generalized to study the relation between covariant and canonical dynamics of loop quantum gravity. On one hand, a graphical derivation of the partition function of the generalized Euclidean Engle-Pereira-Rovelli-Livine (EPRL) spin-foam model is presented. On the other hand, the action of a Euclidean Hamiltonian constraint operator on certain spin network states is calculated by graphical method. It turns out that the EPRL model can provide a rigging map such that the Hamiltonian constraint operator is weakly satisfied on certain physical states for the Immirzi parameter $\beta=1$. In this sense, the quantum dynamics between the covariant and canonical formulations are consistent to each other.

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Jinsong Yang, Cong Zhang, Yongge Ma. 2021-02-11. Relating spin-foam to canonical loop quantum gravity by graphical calculus. https://doi.org/10.1103/physrevd.104.044025

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