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Difference between QED & QCD Vacuum

  1. Jun 16, 2013 #1
    Hi pf, i have been wondering what differentiates QED Vacuum from QCD Vacuum? How would u explain its implications? I mean, how can u define pure vacuum in 2 ways?
     
  2. jcsd
  3. Jun 30, 2013 #2
    no reply..what does that imply...:p
     
  4. Jun 30, 2013 #3

    Bill_K

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    The difference is, QED vacuum contains no electrons, while QCD vacuum contains no quarks. :smile:
     
  5. Jun 30, 2013 #4

    tom.stoer

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    There are several differences. The first one is that in low-energy QCD there is a phase with broken chiral symmetry indicated by order parameter (the so-called quark condensate) with non-vanishing expectation value

    ##\langle \bar{q} q \rangle > 0##

    whereas in QED the electron-positron expectation value vanishes

    ##\langle \bar{\psi} \psi \rangle = 0##
     
  6. Jul 1, 2013 #5
    ok..fine..then would you please explain the QED vacuum and the creation of virtual particles and more about vacuum fluctuations?
     
  7. Jul 1, 2013 #6

    tom.stoer

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    What is your background in physics and your knowledge in quantum field theory?
     
  8. Jul 2, 2013 #7
    well.nothing much..just 12th grade..nd beginner of quantum physics...
     
  9. Jul 2, 2013 #8

    tom.stoer

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    OK.

    In quantum field theory one introduces a so-called vacuum state |vac>. This is not trivial mathematically, but the main idea is that
    - the vacuum state is the state with lowest energy
    - the vacuum state is empty, so the are no particles present

    1) Now one can calculate the energy expectation value (in a finite volume) and one can calculate the expectation value for the particle numbers (particles species s, e.g. electrons and positrons, photons, quarks, gluons). One expectes something like

    ##\langle H \rangle_\text{vac} = \langle\text{vac} | H | \text{vac}\rangle = 0##
    ##\langle N_s \rangle_\text{vac} = \langle\text{vac} | N_s | \text{vac}\rangle = 0##

    where H and N are so-called operators which define energy and particle number.

    If you do that for QED (for s = electrons, positrons and photons) you find zero (as expected).

    But for QCD the two definitions do not coincide!!

    So one has a vacuum state with lowest energy 0, but for which the expectation value of N does not vanish. So the two equations become

    ##\langle H \rangle_\text{vac} = \langle\text{vac} | H | \text{vac}\rangle = 0##
    ##\langle N_s \rangle_\text{vac} = \langle\text{vac} | N_s | \text{vac}\rangle \neq 0##

    The so-called quark condensate which I introduced in the previous post is something that measure the quark content of the vacuum. So the non-vanishing of this condensate means that the vacuum (defined as the state with lowest energy) is not empty.

    2) There is a related phenomenon, namely the excitatons of the vacuum. In quantum field theory these quantized excitatons are interpreted as particles.

    In QED one can find states with arbitrary small energy ε>0 (ε can be any positive number). This is rather simple b/c the energy of a photon is just E=hf, so a single photon with small frequency f (long wave length λ) defines such a state

    ##\langle f| H | f \rangle = hf##

    Again in QCD the situation is different. There is no such state with arbitrary small but non-zero energy ε. Adding a single excitatation (a quark, a gluon) results in an unphysical state which is forbidden due to symmetry reasons and due to (infinite) energy. So in QCD there is a mass-gap, which means that one must add a rather large energy (a few hundred MeV) to find the next state above the vacuum state.

    3) In order not t confuse you too much I due not (yet) discuss exceptions to 2) which are closely related to 1)
     
  10. Jul 2, 2013 #9
    this is awesome..though i wont get all of it now...but still, i will. thanks a lot...its wonderful..
     
  11. Jul 3, 2013 #10

    Bill_K

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    Ok then, if it is not zero, what is its value?
     
  12. Jul 3, 2013 #11

    tom.stoer

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    I was cheating a little bit b/c one does not determine <N> but the (flavor-specific) quark condensate; afaik the (ren.-scheme dep.) values are in the range of 300 MeV3; afaik in two-flavor QCD the value can be related to the pion mass and decay constant via the Gell-Mann–Oakes–Renner relation, e.g. in current algebra and chiral perturbation theory; there should be lattice gauge calculations as well.

    I have to find some references.
     
    Last edited: Jul 3, 2013
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