Coordinate light-cone-ordered perturbation theory

TL;DR

This paper reviews coordinate space light-cone-ordered perturbation theory (C-LCOPT), highlighting its path-based approach and extension from amplitudes to cross sections, offering a coordinate-space perspective on light-cone perturbation methods.

Contribution

It introduces a coordinate-space formulation of light-cone-ordered perturbation theory that uses paths instead of intermediate states, extending its application to cross sections.

Findings

Path denominators relate to minus coordinate differences and light-cone distances.

Method extends amplitude techniques to cross sections.

Coordinate-space approach offers new insights into perturbation theory.

Abstract

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.