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 $A^+=0$ where

$A^+ (x^0,x^1,x^2,x^3) = A^0 (x^0,x^1,x^2,x^3) +A^3 (x^0,x^1,x^2,x^3)$

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

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

where $p^+$ is a constant and $\tau$ 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).

See also

• light cone coordinates

References

1. The light cone gauge Samir D. Mathur
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