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We present the first complete derivation of the well-known asymptoticexpansion of the SU(2) 6j symbol using a coherent state approach, in particularwe succeed in computing the determinant of the Hessian matrix. To do so, wesmear the coherent states and perform a partial stationary point analysis withrespect to the smearing parameters. This allows us to transform the variablesfrom group elements to dihedral angles of a tetrahedron resulting in aneffective action, which coincides with the action of first order Regge calculusassociated to a tetrahedron. To perform the remaining stationary pointanalysis, we compute its Hessian matrix and obtain the correct measure factor.Furthermore, we expand the discussion of the asymptotic formula to next toleading order terms, prove some of their properties and derive a recursionrelation for the full 6j symbol.

Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions