# nobel

Document Sample

```					               infinity

Gerard ’t Hooft, Nobel     Lecture 1999
k
q           

k q
d k 2
1
 (k  m2 )((k  q)2  m2 )
4


What does
Renormalizability
Mean ???

Understanding Small
Distance Behavior !!
The Differential Equation
x   dx
    = velocity
t   dt
Discretized Space   and   Time
Mass and Charge Renormalization
-

+



0
+
Bare  Observed           Bare Observed
Charge Charge         -   Mass Mass
Keeping the Observed Properties
-
           Fixed
+






Bare Observed          Bare Observed
Charge Charge           Mass Mass
All problems with renormalizing
infinities can
be resolved by considering

The Small Distance Limit

of our theory(ies)
The scale transformation
when particles are quantized ...

g´
Scaling and Dimensions
Examples:  theory
4

2
and: Electro-magnetism, e

, e      2

 distance scale
4              2                        2
10              10            1           10
Negative screening:
Yang-Mills gauge theory

2
g

 distance scale
10 4       10 2       1         102
Chiral theories:
These are theories in which a field
has a fixed length:

Field strength
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
At large distance scales, the        curvature  strong interactions
curvature is weak 
near linearity = weak interactions
distance behaviour:



10 2      1        102
Spontaneous symmetry breaking
( left - right symmetry )
At large distance
At short distance             scales, the situation
scales, our particle           is as described here
theory looks
like this                   This degree of
freedom corresponds to
the Higgs particle



Breaking Rotational Symmetry

Now THIS becomes
an essential degree       And THIS is the
of freedom            Higgs degree of


Freedom
If there were no HIGGS particle in our
theory, then the “Mexican Hat” would
be infinitely steep, or:

M Higgs  
This is exactly like the situation in a
“chiral field theory”:

 F
2       2

Such a theory is ill-defined, since its
small-distance structure runs out of control...
How does force depend on distance ?
Force
Weak:

Electro-magnetic:

       

Strong

EM
Weak
Strong:
q               q     0                    x
The Standard Model
Generation I      Generation II   Generation III

e    e                              
Leptons    e  e
R
  
R
        
R
L                  L                  L
u u u              c c c          t t t
d d dL             s s sL         b b b  L
Quarks
u u u               c c c          t t t
R                  R                  R
d d d               s s s           b b b
                                     Higgs
Gauge
Z0
W

              g
Bosons          W                                     Graviton
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
*  g strong
1
*
*    g Weak
0.5                            *    eElect-Magn
*
*
*
*   *   *   *
*   *   *   *
3       6    9        12     15      18
1 GeV 10 10             10       10    10     10
Super symmetric theories
*  g strong
1
*
*    g Weak
0.5       *                      *    eElect-Magn
*
*
*   *    *    *
*   *    *    *
3       6    9        12     15      18
1 GeV 10 10               10       10    10     10
Super String Theory

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

Otherwise, it is likely to
Royal Swedish
and the explode ….