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

Understand

We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix.

• To do so, we smear the coherent states and perform a partial stationary point analysis with respect to the smearing parameters.
• This allows us to transform the variables from group elements to dihedral angles of a tetrahedron resulting in an effective action, which coincides with the action of first order Regge calculus associated to a tetrahedron.
• To perform the remaining stationary point analysis, we compute its Hessian matrix and obtain the correct measure factor.