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Energy conservation for virtual photon

  1. Aug 4, 2009 #1
    In introducing the concept of 'virtual photon',Halzen Martin writes (ch#1,P#7) "An ekectron emits a photon (the quantum of electromagnetic field) and as a result,recoils in order to conserve momentum.it is clearly impossible to conserve energy as well,so the emitted photon is definitely not a real photon"...

    Why energy and momentum cannot be simoultaneously satisfied?Is momentum conservation is a bit prefferred over energy conservation?
     
  2. jcsd
  3. Aug 5, 2009 #2

    tiny-tim

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    Hi neelakash! :smile:

    To simplify the calculations, let's do it in the frame in which the initial and final velocities of the electron are equal and opposite …

    change in energy-momentum 4-vector = (E,p) - (E,-p) = (0,2p), which is faster than light (infinitely fast, in this case), and so it can't be the energy-momentum 4-vector of a real photon (or a real anything)! :wink:

    (same in any other frame … the change cemes out as (∆E,∆p) with ∆E2 < ∆p2, which isn't allowed)
     
  4. Aug 5, 2009 #3
    I think the statement that "energy is not conserved for a virtual particle" is not right. The 4-momentum including energy is always conserved as the requirement of Lorentz covariance. This is manifest in Feynman diagrams: when we go from the space-time representation to momentum representation, each vertex contributes a delta function which exactly results in 4-momentum conservation.

    The true difference between a real and a virtual particle is, a real particle is on-shell, ie., satisfying Einstein's energy momentum relationship: E^2=m^2+p^2 (with c=1); while a virtual particle does not satisfy this relationship. This difference manifests the difference between classical mechanics and quantum mechanics. A real particle satisfies the classical equation of motion(equivalent to the on-shell condition), so it follows a classical path of motion. A virtual particle is caused by quantum fluctuation, and follows "other paths" in the path integral, so it's off-shell.
     
  5. Aug 5, 2009 #4

    tiny-tim

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    Hi Phiphy! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    ah, but nobody said that "energy is not conserved for a virtual particle" …

    Halzen Martin (ch#1,P#7) says …
    and I said …
    We're all saying that energy-momentum is not conserved for a real particle. :smile:
    Nah … the true difference between a real and a virtual particle is, a real particle is real and a virtual particle isn't. :wink:

    (the clue's in the name! :biggrin:)
     
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