# Light-cone Gauge

1. Nov 12, 2009

### wam_mi

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. Nov 13, 2009

### tom.stoer

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