Physics / research
Renormalized parameters and scale dependence
Separate regulator artifacts from physical predictions through counterterms, renormalization conditions, running couplings, and resummation of large logarithms.
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Module 01 research
Renormalized parameters and scale dependence
Separate regulator artifacts from physical predictions through counterterms, renormalization conditions, running couplings, and resummation of large logarithms.
- 01
A finite prediction can be expressed through different parameter coordinates
Separate regulation, field normalization, counterterms, and physical renormalization conditions.
29 min - 02
Finite subtraction conditions define different useful coordinates
Compare stable-particle pole conditions with MS and modified MS without treating scheme parameters as identical numbers.
29 min - 03
Subtract short-distance subgraphs before the overall divergence
Explain lower-order counterterm insertions and the locality of the remaining ultraviolet subtraction.
29 min - 04
Scale compensation relates running parameters to field normalization
Derive the Callan–Symanzik equation with an explicit anomalous-dimension sign and distinguish scale variation from physical dilation.
29 min - 05
Regulator poles determine finite running through a fixed-bare derivative
Extract a beta function while retaining the engineering term and check higher-pole consistency.
29 min - 06
Run within a theory and match when its active fields change
Integrate a mass anomalous dimension and distinguish threshold matching from automatic heavy-particle decoupling.
29 min - 07
Finite coordinate changes move coefficients while preserving predictions
Transform a beta function and an observable consistently, and identify which perturbative invariants require assumptions.
29 min - 08
One-loop evolution sums an infinite tower of logarithms
Derive a leading-log solution and distinguish resummation from adding unknown fixed-order information.
29 min - 09
Local products require a closed basis and matrix evolution
Renormalize operator insertions and show why Wilson coefficients evolve with a transposed anomalous-dimension matrix.
29 min - 10
Factorial growth exposes information beyond a finite loop expansion
Connect momentum-region logarithms to Borel singularities while separating asymptotic estimates from a nonperturbative definition.
29 min