An efficient algorithm for the Riemannian 10j symbols

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Published 6 March 2002 • Published under licence by IOP Publishing Ltd
, , Citation J Daniel Christensen and Greg Egan 2002 Class. Quantum Grav. 19 1185 DOI 10.1088/0264-9381/19/6/310

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1 Department of Mathematics, University of Western Ontario, London, Ontario, Canada

Dates

  1. Received 30 November 2001
  2. Published

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0264-9381/19/6/1185

Abstract

The 10j symbol is a spin network that appears in the partition function for the Barrett–Crane model of Riemannian quantum gravity. Elementary methods of calculating the 10j symbol require Script O(j9) or more operations and Script O(j2) or more space, where j is the average spin. We present an algorithm that computes the 10j symbol using Script O(j5) operations and Script O(j2) space, and a variant that uses Script O(j6) operations and a constant amount of space. An implementation has been made available on the web.

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10.1088/0264-9381/19/6/310