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B Quantum Manifolds

  1. Jan 30, 2016 #1
    Does the words "Quantum Manifolds" make any sense?

    Can quantum occurs on a manifold?

    Or do you automatically equate manifolds to lorentzian manifold and it becomes a problem of quantum gravity?

    Or can there be manifolds not related to spacetime.. so can quantum on manifold make sense?
  2. jcsd
  3. Jan 30, 2016 #2


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    Staff: Mentor

    What is 'Quantum'?
    I know what manifolds are: mathematical structures used to describe several physical models. Therefore manifolds appear not only in spacetime models. If you like you could even regard every vector space as a manifold.
    So what do you mean by 'Quantum'?
    At its best it is 'something discrete' and not really appropriate as a precisely defined term outside of QFT, QCD or alike. Even quantum gravity is IMO more a popular punchline to describe GUTs than a physically term.
    Therefore we are left with discrete manifolds, i.e. a discrete topology which is rather boring. I don't know whether it is used in physical models. However, there are lattices in QFT. I have no idea whether manifolds are an appropriate concept to deal with them, but I have my doubts.
  4. Jan 30, 2016 #3
  5. Jan 30, 2016 #4
    Does the words "higher dimensional manifolds" make sense? Since quantum has non-local correlations beyond Lorentizian spacetime.. is it not incorrect to say quantum waves use higher dimensional manifolds?
  6. Jan 30, 2016 #5


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    A manifold can have a dimension, so "higher dimensional manifolds" might make sense when it is clear what we're comparing when we say that the dimensionality of one manifold is higher than that of another.
    Neither correct nor incorrect, as this is just meaningless babble.

    This thread is closed.
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