A Confrontation with
description
Transcript of A Confrontation with
![Page 1: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/1.jpg)
Gerard ’t Hooft, Nobel Lecture 1999
infinity
![Page 2: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/2.jpg)
q
k q
k
42 2 2 2
1d ( )(( ) )
kk m k q m
![Page 3: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/3.jpg)
What does Renormalizability
Mean ???
Understanding SmallDistance Behavior !!
![Page 4: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/4.jpg)
The Differential Equation
= velocityxt
dxdt
![Page 5: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/5.jpg)
Discretized Space and Time
Continuous space and Time
![Page 6: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/6.jpg)
Mass and Charge Renormalization
Bare Charge
BareMass
ObservedCharge
ObservedMass
0
+
-
+
-
![Page 7: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/7.jpg)
Bare Charge
ObservedCharge
BareMass
ObservedMass
Keeping the Observed Properties Fixed
+
-
![Page 8: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/8.jpg)
All problems with renormalizing infinities can
be resolved by considering
of our theory(ies)
The Small Distance Limit
![Page 9: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/9.jpg)
The scale transformation
gg´
when particles are quantized ...
![Page 10: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/10.jpg)
Scaling and Dimensions4Examples: theory
410 210 1 210
distance scale
2, e
2and: Electro-magnetism, e
![Page 11: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/11.jpg)
Negative screening: Yang-Mills gauge theory
410 210 1 210
distance scale
2g
![Page 12: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/12.jpg)
Chiral theories:These are theories in which a field
has a fixed length:
Field strength
![Page 13: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/13.jpg)
Compare large distance with small distance:
At large distance scales, thecurvature is weak near linearity = weak interactions
At small distances, strongcurvature strong interactions
The quantum fluctuations at small distancein such a theory undermine its own structure.
Its small-distance behaviour is ILL-DEFINED
![Page 14: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/14.jpg)
Some theories have BAD short distance behaviour:
210 1 210
![Page 15: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/15.jpg)
Spontaneous symmetry breaking( left - right symmetry )
At short distancescales, our particle
theory lookslike this
At large distancescales, the situationis as described here
This degree offreedom corresponds to
the Higgs particle
![Page 16: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/16.jpg)
Breaking Rotational Symmetry
Now THIS becomes an essential degree
of freedomAnd THIS is theHiggs degree of
Freedom
![Page 17: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/17.jpg)
If there were no HIGGS particle in ourtheory, then the “Mexican Hat” would
be infinitely steep, or:
HiggsM This is exactly like the situation in a
“chiral field theory”:2 2F
Such a theory is ill-defined, since itssmall-distance structure runs out of control...
![Page 18: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/18.jpg)
How does force depend on distance ?
Weak:
Strong:
Strong
EMWeak
x
Force
q q
Electro-magnetic:
0
![Page 19: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/19.jpg)
Leptons
Quarks
Generation I Generation II Generation IIIThe Standard Model
Gauge Bosons g
us s
e
u
c
c
b b
b b
t t
0Z
dt
cs
e
u
c t
b
s
W
du t
W
e
u
c t
d
Graviton
L L L
e
u
d
cs
d
s b
dHiggs
L L L
R R R
RRR
![Page 20: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/20.jpg)
CERN
SpS&
LEP* *
![Page 21: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/21.jpg)
Linear Accelerator
Fermilablinear booster
![Page 22: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/22.jpg)
A symmetric object can be slightly out of equilibrium …
![Page 23: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/23.jpg)
An asymmetric equilibrium is unnatural ...
![Page 24: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/24.jpg)
Running Coupling Strengths
*
**
***
*
**
***
strongg
Elect-MagneWeakg
*
*
*
310 610 910 1210 1510 18101 GeV
1
0.5
![Page 25: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/25.jpg)
Super symmetric theories
strongg
Elect-MagneWeakg
*
*
*
*
**
*
**
*
**
***
310 610 910 1210 1510 18101 GeV
1
0.5
![Page 26: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/26.jpg)
Are strings continuous or are they discrete
at tiny distance scales ?
Super String Theory
![Page 27: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/27.jpg)
Otherwise, it is likely toexplode ….
A theory can only be successfulif we understand completelyhow its dynamical variables
behave at the tiniest possibletime- and distance scales
![Page 28: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/28.jpg)
![Page 29: A Confrontation with](https://reader036.fdocuments.us/reader036/viewer/2022062521/56816865550346895ddec2c8/html5/thumbnails/29.jpg)
Otherwise, it is likely toexplode ….
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 SwedishAcademy of Sciences