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Is there any approximation to the two particle density matrix

  1. Jul 28, 2006 #1
    Let phi(x) and phi_dagger(x) be field operators which satisfy the appropriate commutation relations.

    Then is there any analytic approximation for the two particle density matrix given by


  2. jcsd
  3. Jul 28, 2006 #2
    [tex]\langle \phi^{\dagger} (x) \phi^{\dagger} (y) \phi(y) \phi (x) \rangle[/tex]

    I'm not thinking this morning - this is a density matrix?
  4. Jul 28, 2006 #3
    The author calls it the two particle density matrix. The reference is Phys Rev B, Vol 71, 165104 (2005)

    The page number is 165104-3
  5. Jul 28, 2006 #4


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    It most certainly is the field operator version of the density matrix. By the way, this fact has to do with why I called the state |0><0| the "vacuum" in the discussion on the "superposition and kets":

    The best reference I've seen for explaining why this is the case is Julian Schwinger's "Quantum Kinematics and Dynamics", which is a small classic paperback book that is available cheaply at most good physics bookstores and also on Amazon.

  6. Jul 30, 2006 #5


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    NO, It is a number, a single number. It is neither a density nor a matrix.

    the phi's are operator-valued distributions, putting them inside < |...| > gives you a number.



    Note from Hurkyl: I fixed the formatting tags so that this will display properly
    Last edited by a moderator: Jul 30, 2006
  7. Jul 31, 2006 #6
    Depending on the theory, perturbation theory...? And yeah, it's an amplitude not a density matrix.
  8. Jul 31, 2006 #7


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    See, for example, equation (5) of:

    No reason to argue over terminology. And [tex]\rho(x,x')[/tex] is a lot more complicated than just a number.

    Last edited: Jul 31, 2006
  9. Aug 3, 2006 #8


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    Last edited: Aug 4, 2006
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