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A What is the most general mathematical framework for quantum

  1. Dec 9, 2016 #1
    1.- The hilbert space approach does not include distributions (free particle, for example) nor mixed states.
    2.- The C* algebra approach does not account for unbounded operators.
    3.- Rigged Hilbert space approach does not include mixed states.

    I'm not sure about path integral formulation... so I ask.... What is the most general mathematical framework for quantum mechanics
     
  2. jcsd
  3. Dec 9, 2016 #2
    Maybe such mathematical framework cannot exist because it would imply the existance of number operators, hereby violating Gödels incompleteness theorem?
     
  4. Dec 9, 2016 #3

    George Jones

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    Lfqm, why do you think 1. and 3. don't include mixed states?
     
  5. Dec 9, 2016 #4

    vanhees71

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    I'd say all three approaches together make up a consistent rigorous mathematical framework for non-relativistic QT.
     
  6. Dec 9, 2016 #5
    I just started reading a bit on operator algebra's and apparently you need c*-algebra's to deal with situations where an infinite amount of particles are present, as in the thermodynamic limit. (http://www.springer.com/us/book/9783540170938)
     
  7. Dec 9, 2016 #6

    bhobba

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    Off course it does. That's because states are not elements of a vector space but are operators.

    Study Ballentine.

    This book gives our most powerful, complete and rigorous formulation:
    https://www.amazon.com/Geometry-Quantum-Veeravalli-Seshadri-Varadarajan/dp/0387493859

    In practice most physicists use Diracs formulation which is made rigorous by the rigged hilbert space approch.

    Thanks
    Bill
     
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