Lecture 16-17 Notes:
07 / 27 and 07 / 28
Particle physics
Quantum electrodynamics
On a microscopic level, electromagnetic interactions between electrons can be viewed as
the electrons exchanging photons.
One electron emits a photon, and another absorbs it:
A drawing like this is called a
Feynman diagram
.
It corresponds to a well-defined
mathematical expression that can be used to determine the probability of the electrons
interacting in a particular way.
Note that this is somewhat similar to a diagram for a
chemical reaction that has two electrons in the initial and final state, and two electrons
and a photon in the intermediate state:
The photon allows for transfer of energy and momentum between the two electrons.
We
label the electrons' initial 4-momenta
P
1
and
P
2
,
the final 4-momenta
Q
1
and
Q
2
, and the
4-momentum of the photon
K
:
The 4-momentum is conserved at every vertex (point of interaction between a photon
and an electron):
if an electron emits a photon with 4-momentum
K
, its own 4-
momentum decreases by
K
, while the 4-momentum of the electron that absorbs the
photon is increased by
K
.
This ensures that the 4-momentum for the overall process is
conserved:
Q
1
+ Q
2
= P
1
+ P
2
.

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*Sign up*The photon appears as an intermediate in the process, but not in the initial or the final
state.
Intermediate particles like this are known as
virtual particles
.
Particles that are
actually observed either in the initial or in the final state are known as
real particles
.
Real particles obey the energy-momentum relationship
E
2
= p
2
c
2
+ m
2
c
4
(
E = pc
for the
massless photon), but the energy and momentum of virtual particles can deviate from
this relationship.
However, the process depicted in the diagram is more likely to occur
for small deviations than for large ones.
Because the energies and momenta of the electrons change due to the exchange of the
photon, the paths of the electrons change direction as a result of this reaction.
Calculating exactly how the photons and electrons behave from the Feynman diagrams
gives the same results as classical electrodynamics, provided we look at the average
behavior of a large number of photons and electrons rather than individual particles.
Anti-particles
The arrows on the electron lines show the direction of negative charge flow.
If the arrow
points to the right (forward in time), then negative charge flows in the direction of the
particle's motion, just as we expect for a moving electron.
It turns out we can turn the
arrow backwards.
Then, the negative charge follows in a direction opposite to the
particle's motion, which corresponds to a positively charged particle.
The positively
charged counterpart of an electron is known as a
positron
.
The positron has exactly the same properties as an electron (mass, interactions, etc)

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