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Creation/Ann operators acting on <x|p>

  1. Aug 24, 2011 #1
    What does it mean for a creation or annihilation operator to act on the state <x|p>. For example:

    [tex] a_p e^{ip \cdot x} [/tex]
     
  2. jcsd
  3. Aug 24, 2011 #2
    This is not a state. It's just a number. In the second formula you have an operator multiplied by a number.
     
  4. Aug 24, 2011 #3
    Ok, will try to give it in context.

    What does it mean to write a free field scalar as a linear sum of creation and annihilation operators like this?

    [tex]

    \int \frac{d^3 p}{{(2\pi)}^3}\frac{1}{\sqrt{2\omega_p}} [ a_p e^{ip \cdot x} + a_p^\dagger e^{-ip \cdot x} ]
    [/tex]

    What is the creation / annihilation operator role in this, it ends up acting on the amplitude...

    [tex] a = \sqrt{\frac{\omega}{2}}q + \frac{i}{\sqrt{2\omega}}p [/tex]
     
    Last edited: Aug 24, 2011
  5. Aug 24, 2011 #4
    This is a functional transform, much just like the Fourier transform. You have a bunch of creation/annihilation operators that depend on a parameter p. You transform them into another operator set that depends on x.

    Annihilation operators here do not "act" on anything. Rather, they are a subject of transformation. The result of the transformation is another operator that may act on something.
     
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