Digging into the intuition for spinors, and having been reading some
elementary topology, can anyone tell me whether the 4-Pi rotation for
the identity of spinors is (closely?) related to the non-orientability
of the projective plane? For a simpler example, it would take 4-Pi
transit of a Moebius band to regain an original orientation.
The demonstration of the orientation-entanglement relation in real 3
space (eg in MTW, p. 1148-9) shows how a 4-Pi rotation can be required
for identity in E3, but I'm less clear on why it should apply to the
complex projective plane (for electron spin states etc.), which (in my
ignorance of advanced math) I would expect to be orientable. Any
(simply explained) advice would be much appreciated.
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