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

Carlo Marzo

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.

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

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.
Paper Structure (20 sections, 32 equations, 12 figures)

This paper contains 20 sections, 32 equations, 12 figures.

Table of Contents

  1. Introduction
  2. poles $=$ dof
  3. Fields, ghosts and tachyons
  4. Projection operators and the saturated propagator
  5. Kummitus: raison d'être
  6. Kummitus: Method
  7. AI assistance and spurious poles
  8. Usage and examples
  9. Helicity 1: Maxwell Theory
  10. Massless spin-2: Einstein theory and helicity decomposition
  11. TDIFF is enough
  12. Massive spin-2: Fierz-Pauli
  13. Gauge-symmetric massive spin-2 - Part 1
  14. Gauge-symmetric massive spin-2 - Part 2
  15. Massless spin-3: Fronsdal
  16. ...and 5 more sections

Figures (12)

  • Figure 1: Saturated propagator and (two) residues for the Maxwell theory. Output from the provided notebook Models.nb.
  • Figure 2: Saturated propagator and residues for Einstein quadratic Lagrangian
  • Figure 3: Saturated propagator for Einstein theory in helicity basis.
  • Figure 4: Massless and massive propagation under linear transversal diffeomorphism.
  • Figure 5: Masses and the five residues for the propagator of Fierz-Pauli theory from Kummitus
  • ...and 7 more figures