A Confrontation with

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A Confrontation with
infinity
Gerard t Hooft, Nobel
Lecture 1999
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What does Renormalizability Mean ???
Understanding Small Distance Behavior !!
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The Differential Equation
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Discretized Space and Time
Continuous space and Time
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Mass and Charge Renormalization
Observed Charge
Observed Mass
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Keeping the Observed Properties Fixed
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All problems with renormalizing infinities
can be resolved by considering
The Small Distance Limit
of our theory(ies)
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The scale transformation
when particles are quantized ...
g
g
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Scaling and Dimensions
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Negative screening Yang-Mills gauge theory
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Chiral theories
These are theories in which a field has a fixed
length
Field strength
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Compare large distance with small distance
The quantum fluctuations at small distance in
such a theory undermine its own structure. Its
small-distance behaviour is ILL-DEFINED
At small distances, strong curvature ? strong
interactions
At large distance scales, the curvature is weak
? near linearity weak interactions
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Some theories have BAD short distance behaviour
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Spontaneous symmetry breaking
( left - right symmetry )
At large distance scales, the situation is
as described here
At short distance scales, our particle theory
looks like this
This degree of freedom corresponds to the
Higgs particle
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Breaking Rotational Symmetry
Now THIS becomes an essential degree of
freedom
And THIS is the Higgs degree of Freedom
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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...
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How does force depend on distance ?
Force
Weak
Electro-magnetic
Strong
EM
Weak
Strong
x
0
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The Standard Model
Generation I
Generation II
Generation III
Leptons
R
R
R
L
L
L
L
L
Quarks
R
R
R
g
Gauge Bosons
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CERNSpSLEP


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Linear Accelerator
Fermilab linear booster
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A symmetric object can be slightly out of
equilibrium
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An asymmetric equilibrium is unnatural ...
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Running Coupling Strengths
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0.5
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Super symmetric theories
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0.5
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Super String Theory
Are strings continuous or are they
discrete at tiny distance scales ?
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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 .
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With thanks toM. Veltman (teaching)C.T.
de Laat (animation)my wife and the rest of my
family (support)many other physicistsand
the Royal SwedishAcademy of Sciences
Otherwise, it is likely to explode .