Energy Scale Cutoff Control (Λ)
QED Vacuum Polarization
Drag scale slider to integrate out high-momentum degrees of freedom between UV cutoff (ΛUV) and IR scale (μ).
IR Scale (μ = 0.00051 GeV)
Current Λ: 1000.00 GeV
UV Cutoff (ΛUV = 1000.00 GeV)
BARE COUPLING (g0)
0.1000
EFFECTIVE g(Λ)
0.1000
Momentum-Space Shell Integrator
High-frequency fluctuations (k ∈ [Λ-dΛ, Λ]) integrated out
Retained States (k < Λ)
Integrated Shell (dΛ)
Wilsonian RG Trajectory & Phase Space
Running coupling trajectory g(t) & Beta-function β(g)
β(g) = +0.00133
Fixed Point:
g* = 0 (Gaussian IR)
Operator:
Marginal / Marginal-Relevant
Initial Boundary Parameters
0.10
0.05
Beta Function Formulation
β(g) = μ (dg / dμ) = (g3) / (12 π2)
QED exhibits screening: as energy scale μ decreases, virtual electron-positron pairs shield charge, reducing effective g(Λ).
Effective Field Theory Map
Export calculated Wilsonian action parameters, flow trajectory, and energy cutoffs as canonical JSON / PNG summary.
Validated Execution Proof & RG Metrics
Active Regime
QED (U(1))
Bare Coupling g0
0.1000
Effective Coupling g(Λ)
0.1000
Landau Pole / Scale Limit
> 1.0e+10 GeV
Observing momentum scale flow: Initial UV cutoff at 1000.00 GeV down to IR observation scale.