Light-cone coordinates: Difference between revisions

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m (r2.7.1) (robot Adding: ko:빛원뿔 좌표계)
Both x<sup>+</sup> and x<sup>-</sup> can act as "time" coordinates.
 
One thing nice thing about light cone coordinates is that the causal structure is partially included into the coordinate system itself.
 
A boost in the tx plane shows up as <math>x^+ \to e^{+\beta}x^+</math>, <math>x^- \to e^{-\beta}x^-</math>, <math>x^i \to x^i</math>. A rotation in the ij-plane only affects <math>x_\perp</math>. The parabolic transformations show up as <math>x^+ \to x^+</math>, <math>x^- \to x^- + \delta_{ij}\alpha^i x^j + \frac{\alpha^2}{2} x^+</math>, <math>x^i \to x^i + \alpha^i x^+</math>. Another set of parabolic transformations show up as <math>x^+ \to x^+ + \delta_{ij}\alpha^i x^j + \frac{\alpha^2}{2} x^-</math>, <math>x^- \to x^-</math> and <math>x^i \to x^i + \alpha^i x^-</math>.
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