Light-cone coordinates: Difference between revisions

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Assume we're working with a (d,1) Lorentzian signature.
 
Instead of the standard coordinate system (using [[Einstein notation|Einstein notation]])
:<math>ds^2=-dt^2+\delta_{ij}dx^i dx^j</math>,
with <math>i,j=1,\dots,d</math> we have
:<math>ds^2=-2dx^+dx^- + \delta_{ij}dx^i dx^j</math>
with <math>i,j=1,\dots,d-1</math>, <math>x^+=\left[frac{t+x\right]/}{\sqrt{2}}</math> and <math>x^-=\left[frac{t-x\right]/}{\sqrt{2}}</math>.
 
Both x<sup>+</sup> and x<sup>-</sup> can act as "time" coordinates.
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