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A Confrontation with. infinity. Gerard ’t Hooft, Nobel Lecture 1999. What does Renormalizability Mean ???. Understanding Small Distance Behavior !!. The Differential Equation. Discretized Space and Time. Continuous space and Time. -. +. Bare

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slide1

A Confrontation with

infinity

Gerard ’t Hooft, Nobel Lecture 1999

what does renormalizability mean
What does RenormalizabilityMean ???

Understanding Small

Distance Behavior !!

discretized space and time
Discretized Space and Time

Continuous space and Time

mass and charge renormalization

-

+

Bare

Mass

Bare

Charge

+

-

Mass and Charge Renormalization

Observed

Charge

Observed

Mass

keeping the observed properties fixed

-

+

Bare

Charge

Observed

Charge

Bare

Mass

Observed

Mass

Keeping the Observed Properties Fixed
slide8

All problems with renormalizing infinities can

be resolved by considering

The Small Distance Limit

of our theory(ies)

the scale transformation
The scale transformation

when particles are quantized ...

g

chiral theories
Chiral theories:

These are theories in which a field

has a fixed length:

Field strength

compare large distance with small distance
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

slide15

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

breaking rotational symmetry
Breaking Rotational Symmetry

Now THIS becomes

an essential degree

of freedom

And THIS is the

Higgs degree of

Freedom

slide17

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
How does force depend on distance ?

Force

Weak:

Electro-magnetic:

Strong

EM

Weak

Strong:

x

0

the standard model

L

Higgs

Graviton

The Standard Model

Generation I

Generation II

Generation III

R

R

R

Leptons

L

L

L

L

L

Quarks

R

R

R

g

Gauge

Bosons

linear accelerator
Linear Accelerator

Fermilab

linear booster

running coupling strengths

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

Running Coupling Strengths

1

0.5

super symmetric theories

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

Super symmetric theories

1

0.5

super string theory
Super String Theory

Are strings continuous or

are they discrete

at tiny distance scales ?

slide27

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 ….

slide29

With thanks to:M. 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 ….