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Classical and quantum fields

  1. May 14, 2014 #1
    In QFT, all particles can be interpreted as excitations of some fundamental quantum fields in the vacuum. This is the quantum picture. But in classical world, only photons and gravitons have classical counterparts. How to explain this? The common feature of these two is that they are intermediate particles of long-range interactions. But This is far from satisfactory to me. So I was wondering whether there is a deeper and better explanation of this problem.
  2. jcsd
  3. May 14, 2014 #2
    Roughly speaking, quantum fields look like classical waves when there are many particles in the same state. So classical electromagnetic waves are states of many photons and classical gravitational waves are states of many gravitons.

    Fermion fields don't have any states that look classical, because you cannot put more than one fermion in the same state. So there is no classical analog of the electron field.

    The W, Z, and Higgs fields are bosonic but they never look classical because these bosons all decay long before you could hope to construct a state containing lots of them. (This is pretty much the same thing as saying that they don't mediate long-range interactions.)

    The gluon field undergoes confinement and so there aren't actually any states that look like gluons, let alone states with many coherent gluons. There are only hadrons and glueballs.
  4. May 14, 2014 #3

    Meir Achuz

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    What do you mean by this? What is "classical" about photons and gravitons?
  5. May 15, 2014 #4
    For the static electric field around an electric charge, how to understand it from the perspective of quantum fields? In the absence of test particle, I guess there is no photons except vacuum bubble. So can we say there is no electric field unless a test particle is placed nearby to have virtual photon exchange?

    Of course we don't have quanta in classical world. I mean the classical wave or field: EM field or radiation, gravitational field or gravitational wave.
  6. May 15, 2014 #5


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    In covariant QED the static Coulomb field is mediated by the scalar and longitudinal photons which exist even in vacuum (where no transverse photons are present).
  7. May 15, 2014 #6
    Doesn't the scalar mode always cancel out the longitudinal mode?
    If there is no test particle, where do the scalar and longitudinal modes end?
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