Gerard ’t Hooft, Nobel Lecture 1999 infinity

What does Renormalizability Mean ??? Understanding Small Distance Behavior !!

The Differential Equation

Discretized Space and Time Continuous space and Time

Mass and Charge Renormalization Bare Charge Bare Mass Observed Charge Observed Mass

Bare Charge Observed Charge Bare Mass Observed Mass Keeping the Observed Properties Fixed + -

All problems with renormalizing infinities can be resolved by considering of our theory(ies) The Small Distance Limit

The scale transformation g g´g´ when particles are quantized...

Scaling and Dimensions

Negative screening: Yang-Mills gauge theory

Chiral theories: These are theories in which a field has a fixed length : Field strength

Compare large distance with small distance: At large distance scales, the curvature is weak  near linearity = weak interactions At small distances, strong curvature  strong interactions The quantum fluctuations at small distance in such a theory undermine its own structure. Its small-distance behaviour is ILL-DEFINED

Some theories have BAD short distance behaviour:

Spontaneous symmetry breaking ( left - right symmetry ) At short distance scales, our particle theory looks like this At large distance scales, the situation is as described here This degree of freedom corresponds to the Higgs particle

Breaking Rotational Symmetry Now THIS becomes an essential degree of freedom And THIS is the Higgs degree of Freedom

If there were no HIGGS particle in our theory, then the “Mexican Hat” would be infinitely steep, or: This is exactly like the situation in a “chiral field theory”: Such a theory is ill-defined, since its small-distance structure runs out of control...

How does force depend on distance ? Weak: Strong: Strong EM Weak x Force Electro-magnetic: 0

Leptons Quarks Generation IGeneration IIGeneration III The Standard Model Gauge Bosons g Graviton LLL Higgs L LL RRR RRR

CERN SpS & LEP * *

Linear Accelerator Fermilab linear booster

A symmetric object can be slightly out of equilibrium …

An asymmetric equilibrium is unnatural...

Running Coupling Strengths * * * * * * * * * * * * * * * 1 0.5

Super symmetric theories * * * * * * * * * * * * * * * 1 0.5

Are strings continuous or are they discrete at tiny distance scales ? Super String Theory

Otherwise, it is likely to explode …. A theory can only be successful if we understand completely how its dynamical variables behave at the tiniest possible time- and distance scales

Otherwise, it is likely to explode …. With thanks to: M. Veltman (teaching) C.T. de Laat (animation) my wife and the rest of my family (support) many other physicists and the Royal Swedish Academy of Sciences