Coordinate light-cone-ordered perturbation theory

We review the development of light-cone-ordered perturbation theory in coordinate space (C-LCOPT). Compared to light-cone-ordered perturbation theory in momentum space (LCOPT), the role of intermediate states in LCOPT is played in C-LCOPT by paths, which are ordered sequences of lines and vertices that connect pairs of external points. Each path denominator of C-LCOPT equals the difference between the separation of the minus coordinates of the beginning and ending points of the path and the sum of the light-cone distances of all lines along the path computed from their plus and transverse coordinates. We observe that this method, originally applied to amplitudes, can be extended to cross sections, which are given in terms of closed paths reminiscent of Schwinger–Keldysh formalisms.