Whitney covering lemma

2013-09-18T01:15:02Z

65.60.211.222: changed the word "cover" to "decompose" Cover implies that open sets are merely contained in such cubes as described, whereas the interesting thing here is that the open set is itself the union of such cubes.

{{refimprove|date=February 2013}}
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.<ref>[http://www.physics.ohio-state.edu/~mathur/lightcone.pdf ''The light cone gauge'' by Prof. Samir D. Mathur]</ref><ref>''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 [http://www.sciencedirect.com/science/article/pii/0550321380900863]</ref>

==Gauge theory==

In [[gauge theory]], light-cone gauge refers to the condition <math>A^+=0</math> where
:<math>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)</math>
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
:<math>X^+(\sigma, \tau) = p^+ \tau</math>
where <math>p^+</math> is a constant and <math>\tau</math> is the worldsheet time.

The advantage of light-cone gauge is that all [[Faddeev–Popov ghost|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 ==
<references />

[[Category:Theoretical physics]]

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Whitney covering lemma