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

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.
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [3]
  1. Wydział Fizyki, Uniwersytet Warszawski, Hoża 69, 00-681, Warsaw (Poland)
  2. (Canada)
  3. (Germany)
  4. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada)
Publication Date:
OSTI Identifier:
22250914
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACTION INTEGRAL; ANNIHILATION OPERATORS; ASYMPTOTIC SOLUTIONS; EIGENSTATES; MATRICES; RACAH COEFFICIENTS; REGGE CALCULUS; SU GROUPS