Penrose on Spin Networks

Here's a classic paper on spin networks that was previously available only in an out-of-print book:

• Roger Penrose, Angular momentum: an approach to combinatorial space-time, in Quantum Theory and Beyond, ed. T. Bastin, Cambridge University Press, Cambridge, 1971, pp. 151–180. Available in PDF and Postscript, or as LaTeX source code.

This electronic version was prepared by Georg Beyerle. Roger Penrose has given me his permission to make it available here.

Here's another, also prepared by Georg Beyerle:

• Roger Penrose, On the nature of quantum geometry, in Magic Without Magic, ed. J. Klauder, Freeman, San Francisco, 1972, pp. 333–354. Available in PDF and Postscript, or as LaTeX source code.

If you find typos in either of these two papers, please let me know! Various people have caught typos so far, and I was able to fix them. For example, Milan Vandrovec caught a lot of them.

Note: above Figure 2 of "Angular momentum: an approach to combinatorial space-time" the list of numbers "3, 2, 3" is in the original paper. This might be a typo for "1, 2, 3", although "0, 1, 2, 3" would make even more sense.

Here are two more papers on spin networks by Penrose:

• Roger Penrose, Applications of negative dimensional tensors, in Combinatorial Mathematics and its Applications, ed. D. Welsh, Academic Press, New York, 1971, pp. 221–244. Available in PDF.
• Roger Penrose, Combinatorial quantum theory and quantized directions, in Advances in Twistor Theory, eds. L. Hughston and R. Ward, Pitman Advanced Publishing Program, San Francisco, 1979, pp. 301–307. Available in PDF.

Here are some notes by Penrose, apparently passed from him to Lee Smolin, then to Scott Morrison, and then to me:

• Roger Penrose, Theory of quantized directions, handwritten notes, 1971. Available in PDF.

• John P. Moussoris, Quantum Models of Space-Time Based on Recoupling Theory, Ph.D. thesis, Department of Mathematics, University of Oxford, 1983. Available in PDF. Errata found by John Barrett, also in PDF.

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