Can gauge symmetry breaking reveal hidden interactions at low temperatures?

Garlic
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Can there be interactions that are symmetric under low temperatures but exhibit spontaneous symmetry breaking under extremely low temperatures? (Maybe that symmetry breaking temperature is so low that it couldn't be discovered in experiments)
Does electromagnetism split into electricity and magnetism under ideal conditions?
 
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Electromagnetism "splits into" electricity and magnetism under ordinary conditions. Pre-19th century, they were thought to be two different phenomena.
 
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I don't think electromagnetism splits into anything.

Its four-vector potential just has a temporal component, and three spatial ones. We perceive temporal component as electrostatic potential, and spatial ones as magnetic vector potential. But they are not independent or invariant fields, they are projections of a single field onto your particular frame of reference's time and space subspaces

That's why stationary charges have only electric field (temporal component), but when observer starts moving, magnetic field "magically appears" - by Lorentz transform, for this observer temporal component partially "spilled into" spatial ones.
 
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I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...
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