Interactive Visualizations
Simulation Results
Explore the Pareto frontiers and scheme-invariance results from our multi-objective optimization
Understanding Renormalization
WHAT: Renormalization is how we handle infinities in quantum field theory calculations. Different calculation methods (called "schemes") give the same physical predictions even though intermediate steps look different.
WHY: When physicists calculate particle interactions, they get infinite answers at first. Renormalization is the systematic way to extract finite, measurable predictions. Testing whether different schemes agree validates our theoretical framework.
HOW: We compare three popular schemes (MS-bar, on-shell, MOM) using multi-objective optimization. Each scheme uses different mathematical tricks to handle infinities, but all should predict the same physics.
RESULTS: The graph shows different renormalization scales (mu) plotted against how much schemes disagree. Lower values mean better agreement between methods.
IMPLICATIONS: Near-zero invariance penalties prove that our theory is self-consistent. Physical predictions don't depend on which calculation method we choose - a fundamental requirement for quantum field theory to be a valid description of nature.
QFT Renormalization Scheme Optimization
Multi-objective optimization over MS-bar, on-shell, and MOM schemes. The Pareto frontier shows the trade-off between higher-loop corrections and scheme invariance.