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Mar 28, 2011 at 15:16 comment added David Carchedi Thanks for your answer David. This helps me a lot with the big picture.
Mar 28, 2011 at 1:10 comment added José Figueroa-O'Farrill Whereas it is true that in order to be able to write the action for a Dirac fermion (inded, to have Dirac fermions at all!) you need a spin structure, this answer does not address what this has to do with an anomaly. In fact, the anomaly in this case is a global anomaly of a one-dimensional sigma model describing a spinning particle. I believe this is explained in Edward Witten's "Global anomalies in string theory" (as a warm-up example) in his 1985 contribution to the Argonne Symposium on Anomalies, Geometry and Topology, which sadly I do not have with me nor can I find online.
Mar 28, 2011 at 0:27 history answered David Roberts CC BY-SA 2.5