# Inclusive scattering matrix and scattering of quasiparticles

## TL;DR

This paper introduces the concept of an inclusive scattering matrix within quantum theory formulated via L-functionals, linking it to Green functions and enabling analysis of quasiparticle collisions.

## Contribution

It presents a novel formulation of the scattering matrix as an inclusive quantity using L-functionals, connecting it to Green functions and diagrammatic methods.

## Key findings

- Inclusive scattering matrix relates to on-shell Green functions.
- L-functionals provide a simple framework for Keldysh diagrams.
- The approach aids in analyzing quasiparticle collisions.

## Abstract

The quantum theory can be formulated in the language of positive functionals on Weyl or Clifford algebra ($L$-functionals). It is shown that this language gives simple understanding of diagrams of Keldysh formalism (that coincide in our case with the diagrams of thermo-field dynamics). The matrix elements of the scattering matrix in the formalism of $L$-functionals are related to inclusive cross-sections, therefore we suggest the name "inclusive scattering matrix" for this notion. The inclusive scattering matrix can be expressed in terms of on-shell values of generalized Green functions. This notion is necessary if we want to analyze collisions of quasiparticles.