While adding a reference, I noticed that the entry classical field theory is in a sad state.

Hereby I move some old discussion box from there to here:

Ian Durham: I’ve never heard of supergravity as being considered a *classical* theory before. Isn’t the spin structure it is imbued with inherently quantum mechanical in nature? I’ve never even seen it in anything other than a quantum field theory book (i.e. I’ve never seen it in a GR or GR-related book)?

Zoran: criterium on which book is irrelevant. It is easy to see in any treatment, that one has a classical version first and then quantization.

Tim van Beek: There may be some confusion because spin in physics is a quantum phenomenon, and “supertheories” try to unify the treatment of fermions and bosons, who are again pure quantum terms. But that does not imply that e.g. a spin structure on a manifold would be considered to be a “quantum structure”: Take a smooth mainifold and put a bundle structure on it: That is still a “classical object” for mainstream physics. Same thing with supergravity. Both become “quantum objects” if you build a Hilbert space of states and turn your observables into operators on this space, for example (see geometric quantization).

Ian Durham: Well, true, but in my personal experience it doesn’t take on any physical meaning until it is quantized (in this case). In other words, while I’m not necessarily disputing what you’re saying, I’m saying it’s a little misleading to list it under “classical field theory” without some accompanying caveat.

Zoran: it is exactly one of the puproses of the nlab to have a viewpoint which is systematics and not impressionistic. It is very clear where to draw the picture between classical and quantum from the point of view of the theoretical framework and from the point of view of Planck constant. If you had a physical system simulating ANY of these you would see its classical limit h->0 still with supersymmetry in field description. I do not understand what is “physics” here. Why would full picture be physics and the hi energy mod Planck constant ratio limit of its description would not ??

Ian Durham: I’ve done some work in the area of emergence and it is not entirely clear that classical systems automatically appear as h -> 0. M.H. Partovi has recently discovered quantum behavior in macroscopic systems, for instance, so I strongly dispute the usual h -> 0 argument (as do some other people working on emergence).

Tim van Beek: @Ian: Okay, I think I get your point now. What you write about emergence sounds interesting, I think I heard a bit about macroscopic quantum phenomena in (biological) cells. @Zoran: Up to now I always considered (classical) supergravity as a stepping stone to a quantum theory, but not as a valid theory on it’s own. If I get your point, then there is a stronger interpretation that says that the theory makes sense as a classical theory describing fermionic and bosonic matter fields? It would be interesting to make this more precise - well, what I mean is: explain it in a way that even I can understand it - as I wrote before, I thought the very notion of “fermionic” lives in the quantum regime only and does not make any sense in classical physics.

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