Counterterra: Renormalization
Nuclear & Particle Physics arc, page 185 of 193. Back to The Pixelated Physics Universe
Who they are
Counterterra has one line, and says it often: “My infinities are renormalised.”
Counterterra is a character of the Nuclear & Particle Physics arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Renormalisation absorbs divergences into a redefinition of measured mass and charge, leaving finite predictions.
$$ \begin{gathered} m = m_0 + \delta m \\ e = \sqrt{Z_3}\, e_0 \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $m$ | measured (physical) mass | kg |
| $m_0$ | bare mass | kg |
| $\delta m$ | mass counterterm (self-energy) | kg |
| $e$ | measured charge | C |
| $e_0$ | bare charge | C |
| $Z_3$ | photon field renormalisation constant | — |
Sources
Crossovers
Counterterra meets The Vertex Smith (Quantum Electrodynamics Vertex). The Vertex Smith's diagrams give infinite loop corrections. Counterterra absorbs them into the measured mass and charge, leaving finite predictions.
Counterterra meets Tripla (Anomaly That Counts Colours). Counterterra can remove infinities, but Tripla's anomaly survives every renormalisation scheme. It is a real quantum effect, not an artefact.
Counterterra meets Truncalis (Asymptotic Series QED). Counterterra makes each order of the series finite. Truncalis knows that the series as a whole may still diverge. Finite terms do not guarantee a convergent sum.
Wear the lore
Concept keywords: Renormalization, Counterterra, Nuclear & Particle Physics, physics lore, Pixelated Physics