Dear colleagues, what do you think of a possible mathematical analogy between a one-sided surface and a Bose-Einstein condensate?
Interesting Q..There seems a connection from a twist in a two sided strip producing moebius one sided surface and the fact that two states condense to one.
Cheers
Yes, dear Narasim Ramesh, but not only this. For example, one can consider the behavior of a superfluid liquid on the surface of a Mobius strip or a Klein bottle.
Before moving on to the actually proposed statement, let us remind ourselves of the following. The so-called bosonic condensate is actually a condensate of fermionic pairs. Even the Higgs boson, as was recently found, decays into a quark and an antiquark in 58% cases, and after all, quarks are fermions. In the Dirac vacuum, there is a constantly continuing mutual transformation of virtual photons (bosons) and virtual positronium (a pair of fermions). And so on, through Cooper pairs, the BCS theory, and much more.
Let us also recall one interesting property of one-sided surfaces: the self-identical transformation of an orthogonal vector to a one-sided surface is a rotation by 720̊ (4π radians), while for an ordinary two-sided surface - by 360̊ (2π radians).
Now, juxtaposing spin ׀½׀ a rotation by π, and an integer spin of ׀0׀ or ׀1׀ with a rotation by 2 π, we obtain a nontrivial analogy between a bosonic condensate and a one-sided surface.
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