Kummitus: a light-weight toolbox for counting DOF in perturbative QFT

TL;DR

Kummitus is a lightweight, open-source Mathematica toolbox that efficiently computes gauge-invariant propagators in quantum field theories, aiding both research and education.

Contribution

It provides a novel, streamlined algorithmic approach to determine the propagating degrees of freedom in perturbative QFT, complementing existing spectral analysis tools.

Findings

Enables quick computation of gauge-invariant propagators

Facilitates understanding of degrees of freedom in QFT

Serves as an educational resource

Abstract

The consistent construction of quantum field theories beyond the simplest cases requires a precise characterization of the propagating degrees of freedom. These are encoded in the single-pole structure of two-point functions, a connection firmly established through foundational theoretical work of the last century. While high-level programs for spectral analysis are publicly available, we felt the need to complement the existing landscape with a tool that reaches the gauge-invariant propagator by the shortest possible algorithmic path. This is the purpose of \texttt{Kummitus}, an open-source Wolfram Mathematica toolbox designed to do precisely that: compute the (gauge-invariant) propagator. Beyond its utility in research applications, \texttt{Kummitus} is intended as an accessible and transparent resource for the theoretical community, with particular value for pedagogical purposes.