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The Electromagnetic Interaction
In this section we will cover the following topics:
• The Electromagnetic Interaction
• Electromagnetic interactions
• Self Energy Corrections
• QED Calculations
• Gauge Invariance
• Running of α
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The Electromagnetic Interaction
2:20
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The Electromagnetic Interaction
Charged particles interact via photon () exchange
The strength of the interaction is given by the fine
structure constant :
The quantum field theory use to calculate
electromagnetic cross sections is called
Quantumelectrodynamics (QED)
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Electromagnetic Interactions
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Photoelectric Effect
Rutherford Scattering
 ~ 2
~
cross section
Bremsstrahlung
 ~ 3
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Electromagnetic Interactions
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Pair Production
Compton Scattering
 ~ 3
 ~ 2
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Self Energy Corrections
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 ~ α2
 ~ 2
Self-energy corrections contribute to
the mass and charge of the electron.
In QED the mass and charge
become infinite → use principle of
renormalisation to redefine the mass
and charge to their physical values
which cancels the infinities
 ~ α4
Charge and mass look
different at this point
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Renormalization
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QED Calculations
The Magnetic Moment of the electron
First
order
Higher
orders
and so on . . .
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QED Calculations
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QED calculations give incredibly accurate values
The theoretic result, in Bohr Magneton (9.27 × 10-24 JT-1) is:
First order
Higher orders
= 1.001 159 652 307 Theoretical result
± 0.000 000 000 110
Compared with:
= 1.001 159 652 193 Experimental result
± 0.000 000 000 010
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Gauge Invariance
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QED also has Gauge Invariance – independent of an absolute
potential or gauge – only potential differences matter
Global Gauge
Transformation
Electron just
sits there
Raise potential by
10V everywhere
Local Gauge
Transformation
Electron still
sits there
Raise potential by 10V
on one plate only
Electron just
sits there
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Electron starts
to move
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Gauge Invariance
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Changing the potential differently at different places causes the electric
field to change
Charged electron moves → causes a magnetic field to compensate
Combination of changing electric and magnetic fields → photons
Mathematically we allow the phase of the electron to vary at each
point in space where f(x, t) is some arbitrary function:
Local gauge transformations give rise to forces and field quanta
In QED changing potential/phase → photons
In QCD changing colours → gluons
Believe all theories of fundamental fields should be
renormalisable gauge theories
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Running of α
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The strength of the EM coupling given by the electronic charge e
At large distance
electron has charge
-1.6×10-19C
As we look closer we
see that close to the
bare e– there are
virtual e+e– pairs with
the e+ on average
closer to the original
e– → vacuum
polarisation
Q–
Q– + 4q+
Q– + 8q+
Bare electron is screened by +ve charges. Charge appears to
decrease as distance increases (lower energy)
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Running of α
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Normally (low energy, large distance):
At the Z0 mass (higher energy, shorter distance):
(larger)
i.e.  'runs' as did S
but less so and in the
opposite direction
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