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Is there a sort of potential field that can possibly result in paths that are globally non-holonomic with respect to a symmetry of Euclidean space? Iirc things like Aharonov Bohm and a spin-field coupled Hamiltonian for fermions only have non-holonomy on SU(2).
Euclidian space is completely holonomic, as parallel transport is no issue there. So I would imagine no. That’s not to say we can’t have non-holonomic embeddings in Espace like the Möbius strip.
Iirc (spec. rel) the EM 4-pot can be treated like a curvature on Minkowski so you can get Dirac/etc from the free theory by just using a covariant deriv (d-ieA) where the deriv goes. So is what youre saying that any potential treatable like this won't get me what I'm looking for?
I’m curious, take your Time indep Schrodinger and consider time evolution of (for simplicity) an eigenstate (finite level also). Is this parallel transport on the Hilbert space?
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Then after "walking in a circle" (i.e. 2π radians), you will actually be upside-down.
