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A new path integral representation of Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model is derived by employing the theory of unitary representation of SL(2,$\mathbb{C}$).
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W. Kamiński, M. Kisielowski and J. Lewandowski. spinfoams for all loop quantum gravity. Class. Quant. Grav. 27 (2010) 095006
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E. Magliaro and C. Perini. Emergence of gravity from spinfoams. Europhys. Lett. 95 (2011) 30007
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