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Free keywords:
Mathematical Physics, math-ph,General Relativity and Quantum Cosmology, gr-qc,Mathematics, Mathematical Physics, math.MP
Abstract:
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.
Furthermore, we expand the discussion of the asymptotic formula to next to
leading order terms, prove some of their properties and derive a recursion
relation for the full 6j symbol.
