In physics, particularly special relativity, light-cone coordinates, introduced by Paul Dirac and also known as Dirac coordinates, are a special coordinate system where two coordinate axes combine both space and time, while all the others are spatial.

A spacetime plane may be associated with the plane of split-complex numbers which is acted upon by elements of the unit hyperbola to effect Lorentz boosts. This number plane has axes corresponding to time and space. An alternative basis is the diagonal basis which corresponds to light-cone coordinates.

In a light-cone coordinate system, two of the coordinates are with respect to null vectors and all the other coordinates are spatial. The former can be denoted ${\displaystyle x^{+}}$ and ${\displaystyle x^{-}}$ and the latter ${\displaystyle x_{\perp }}$.

Assume we are working with a (d,1) Lorentzian signature.

Instead of the standard coordinate system (using Einstein notation)

with ${\displaystyle i,j=1,\dots ,d}$ we have

with ${\displaystyle i,j=1,\dots ,d-1}$, ${\displaystyle x^{+}={\frac {t+x}{\sqrt {2}}}}$ and ${\displaystyle x^{-}={\frac {t-x}{\sqrt {2}}}}$.

Both ${\displaystyle x^{+}}$ and ${\displaystyle x^{-}}$ can act as "time" coordinates.