well, hmm, can anything like https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment give us such a thing? Obviously, this is the interactions of the spin of the fermions with the U(1) in EM, and not a pure gauge boson effect. But one does wonder the extent to which the classical picture of electric current as a de Rham current (so, distributions, not classical gauge fields) survives into quantisation. I have a vague memory of Scharf's work (https://ncatlab.org/nlab/show/Quantum+Gauge+Theories+--+A+True+Ghost+Story) needing to be very careful around the correct treatment of distribution-valued fields. Stern–Gerlach seems to indicate something survives, and spacetime *looks* non-simply connected from the point of view of the experiment: a flat but nontrivial U(1) gauge field.
But this doesn't really help with CPT symmetry!
Paul Schwahn (npub1zz2…9mhx)
