Math Mapgenerated 2026-10-25 · a354234
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EX-01

a free / quadratic theory — every moment reducible to the two-point function; solvable because nothing interacts

exemplar_kind
object
state
current
created
2026-09-15
topic
probability
source
../exemplars/EX-01-gaussian-as-free-theory.md

Coordinatesthe k=0 origin of the magnitude family (§2) and the fixed point every perturbation expands around — where "quadratic action" meets "fully determined by the covariance

Model forfree field theories, the harmonic oscillator, the normal distribution as maximum entropy, the k=0 term of any perturbation series

The Gaussian is the model of a free theory: a quadratic action, Wick's theorem reducing every moment to the covariance, no interaction to spoil solvability. It is the home for "this is the exactly-solvable part"; whatever is left after subtracting it is, by definition, the interaction. Reaching for it is reaching for the question what is the free piece here, and what does the remainder cost?

generated 2026-10-25the lab index