Consistency check on the fundamental and alternative flux operators in loop quantum gravity |
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Authors: | Jinsong Yang Yongge Ma |
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Institution: | 1. School of Physics, Guizhou University, Guiyang 550025, China2. Department of Physics, Beijing Normal University, Beijing 100875, China |
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Abstract: | There are different constructions of the flux of triad in loop quantum gravity, namely the fundamental and alternative flux operators. In parallel to the consistency check on the two versions of operator by the algebraic calculus in the literature, we check their consistency by the graphical calculus. Our calculation based on the original Brink graphical method is obviously simpler than the algebraic calculation. It turns out that our consistency check fixes the regulating factor \begin{document}$ \kappa_{\rm reg}$\end{document}![]() of the Ashtekar-Lewandowski volume operator as \begin{document}$ \displaystyle\frac{1}{2}$\end{document}![]() , which corrects its previous value in the literature. |
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Keywords: | loop quantum gravity flux operator graphical calculus |
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