# Light cone gauge

In theoretical physics, light cone gauge is an approach to remove the ambiguities arising from a gauge symmetry. While the term refers to several situations, a null component of a field A is set to zero (or a simple function of other variables) in all cases.[1][2]

## Gauge theory

In gauge theory, light-cone gauge refers to the condition ${\displaystyle A^{+}=0}$  where

${\displaystyle A^{+}(x^{0},x^{1},x^{2},x^{3})=A^{0}(x^{0},x^{1},x^{2},x^{3})+A^{3}(x^{0},x^{1},x^{2},x^{3})}$

It is a method to get rid of the redundancies implied by Yang–Mills symmetry.

## String theory

In string theory, light-cone gauge fixes the reparameterization invariance on the world sheet by

${\displaystyle X^{+}(\sigma ,\tau )=p^{+}\tau }$

where ${\displaystyle p^{+}}$  is a constant and ${\displaystyle \tau }$  is the worldsheet time.

The advantage of light-cone gauge is that all ghosts and other unphysical degrees of freedom can be eliminated. The disadvantage is that some symmetries such as Lorentz symmetry become obscured (they become non-manifest, i.e. hard to prove).

## References

1. ^
2. ^ QCD calculations in the light-cone gauge Nuclear Physics B - Volume 165, Issue 2, 24 March 1980, Pages 237–268 by D.J. Pritchard, W.J. Stirling [1]