I recently learned that one of the many lessons that one can learn from the AdS/CFT correspondence is that there could be two classical limits (the bulk with gravity in $D+1$ spatial dimensions, and the boundary theory with $D$ spatial dimensions without gravity) of a quantum theory, namely the underlying quantum gravity theory. (Reference: This paper by Sean Carroll, Page 3) Here, of course, the ''classical'' limit simply means the low energy limit and does not really mean the classical limit as far as I can understand (i.e., the boundary theory is a CFT--not a classical theory in the sense of a non-quantum theory).

I am curious if there can be more than one classical limits of a simple quantum theory (not a quantum gravity theory but a simple non-relativistic quantum theory) in the basic sense of in which one usually means classical limit (i.e. the $h\to0$ limit).

  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/276028/2451 and links therein. $\endgroup$
    – Qmechanic
    Apr 29, 2018 at 12:40
  • $\begingroup$ @Qmechanic Thanks! That pretty much answers my question. Would you mark it as a duplicate or should I simply close/delete? $\endgroup$
    – ACat
    Apr 29, 2018 at 12:47


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