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The inverse transformation is then 

The Minkowski dot product in lightcone coordinates is: 

The length of a vector using lightcone coordinates is then: 

. 

## E.1.2 Eikonality in Light Cone Coordinates 

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Note that the eikonal approximation requires collinear emission, which in turn requires k + ≫ k − (for emitted boson with 4-momentum k ). If this were otherwise, the k z emission would be in the opposite direction of p $^{z}$: p z = 1 $_{2}$( p + − p $^{−}$) ≃ 1 $_{2}$p + = 1 $_{2}$(1 − x ) E $^{+}$; on the other hand k z = 1 $_{2}$( k + − k $^{−}$) must be approximately 1 $_{2}$k + or else the sign is wrong. 

