Shiva and Kali diagrams for composite quantum particle many-body effects

TL;DR

This paper introduces Shiva and Kali diagrams as new visualization tools for many-body effects involving composite quantum particles, addressing limitations of traditional Feynman diagrams.

Contribution

It proposes novel Shiva and Kali diagrams for representing fermion exchanges in composite particles and develops a corresponding many-body operator algebra.

Findings

Shiva diagrams effectively visualize fermion exchanges in cobosons.

Kali diagrams extend this visualization to cofermions.

A new operator algebra formalism is established for composite particles.

Abstract

For half a century, Feynman diagrams have provided an enlightening way of representing many-body effects between elementary fermions and bosons. They however are quite inappropriate to visualize fermion exchanges taking place between a large number of composite quantum particles. We propose to replace them by "Shiva diagrams" for cobosons made of two fermions and by Shiva-like and "Kali diagrams" for cofermions made of three fermions. We also show how these fermion exchanges formally appear in a many-body theory appropriate to composite quantum particles. This theory relies on an operator algebra based on commutators and anticommutators, the usual scalar algebra based on Green functions being valid for elementary bosons or fermions having strict commutation relations, only.