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Light-cone Gauge

  1. Nov 12, 2009 #1
    Hi there,

    How is the light-cone gauge useful for a quantum relativistic particle and for a quantum relativistic string? Why is it important that the light-cone gauge is used? Does it actually simplify the mathematics a lot?

    Thanks
     
  2. jcsd
  3. Nov 13, 2009 #2

    tom.stoer

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    Science Advisor

    Our group studied 1+1 dim QCD in light cone coordinates 15 years ago; you should look for papers from "F. Lenz" and "M. Thies" - unfortunately not in arxiv.

    The main difference in light cone coordinates is the following

    p = (p0, p1, p2, ...) => (p+, p-, p2, ...)

    The dispersion relation for massive particles reads:

    p+ = (... + m²) / 2p-

    where ... means the perpendicular components.

    Due to this dispersion relation for the light cone energy p+ the Dirac sea becomes trivial; there is a unique solution for p+ for given light cone momentum p- ; that means that a sea-particle cannot be excited w/o violation of the light cone momentum. Therefore a "mixing" of quarks and anti-quarks is forbidden = the vacuum structure is trivial.

    Nevertheless you can find non-vanishing condensates, but in a different formalism.

    The light cone gauge for a gauge field A then means

    A- = 0

    It is comparable to the axial gauge, that means
    - one polarization is eliminated completely
    - a "Coulomb potential" arises due to invertion of the Gauss constraint
    Usually one derives a Hamiltonian framework (one has to check for Poincare covariance)

    In some sense the light cone frame is related to the infinite momentum frame.

    As far as I know the light cone approach is not widely used in QCD; the trivial vacuum structure seems to be a benefit when one starts with the calculations, but there are other difficulties like non-dynamical fermionic degrees of freedom (in 1+1 dim. you can see that one component of the spinor is non-dynamical as there is no light cone time derivative) and the non-local light cone energy operator.

    I have no idea how this relates to string theory.
     
    Last edited: Nov 13, 2009
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