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MARKUS KLUTE: Welcome to 8.701.

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So in this lecture, we'll give
you the first introduction

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to Feynman diagram.

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This is part 1 out of a few
sections on Feynman diagrams.

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So this is really meant to
introduce the topic such

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that we can use the
same language to talk

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about Feynman diagrams
before we then later on are

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able to use them as
a tool to calculate

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interesting processes.

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This brings me right
to the essence already.

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What is a Feynman diagrams
and what can it be used for?

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They arise from
pertubative calculations

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of amplitude for reactions.

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And that's exactly how we're
going to use them later on.

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It turns out that the
mathematical terms

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in the perturbation series can
be represented as a diagram.

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And then you can
turn this around

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and use the diagram in order
to perform a calculation.

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So each of the diagrams then
indicates a particular factor

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in the calculation.

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Again, and then you
have a rule which

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allows you to,
after drawing, you

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can then put the pieces
together in order

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to perform [INAUDIBLE]
calculation.

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The derivation of
those tools or rules

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is beyond the content
of this course.

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But I will teach you how
to actually use diagrams

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in order to calculate things.

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So here's one
example of a diagram.

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Let me just put this down
here so you can see this.

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So this is an electron
radiating a photon.

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You see components
like those lines here.

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Those represent particles
with energy and momentum

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also what to consider the spin.

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And they meet at a point.

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This point here is
called a vertex.

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And this is where the
interaction takes place.

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And in this example.

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The vertex is labeled
with a q or e,

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representing the charge, the
electric charge, which gives us

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the strength of the coupling.

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We already discussed when
we talked about units

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that we can express the strength
of the electromagnetic--

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the coupling in QED with
the electric charge.

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And that's shown below again.

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The amplitude then turns out to
be proportional to the charge

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or to this coupling.

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And the diagrams with n vertices
for n of those components

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here get a factor e,
the charge, to the nth

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power in the amplitude,
and e to the second.

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Because if we're going to
calculate a probability,

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you have to square
the amplitude.

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You get a factor of e to 2n.

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Again, don't get
confused-- e is charge.

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So for n vertices, there will
be a factor alpha to the nth

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power for the probability.

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And so since alpha
is 1/137, you see

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that if I want to
do a calculation,

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and diagrams which have n
vertices will be suppressed,

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will not contribute
much to our perturbation

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serious because alpha is
much, much smaller than 1.

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So this is already an
interesting finding.

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Can restrict yourself to
calculating diagrams which

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have a couple of
vertices or n vertices,

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but you don't have to
calculate the entire series.

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You want to measure
your calculation

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with experimental findings.

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Interesting here--
antiparticles.

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If you have a specific
vertex and you calculated it,

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it can be reused.

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It can be reused for
example by replacing

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a particle with an
antiparticle or by re-labeling.

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One thing I haven't
explained to you yet,

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you have to define
when you write them

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which is the direction of time.

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We'll come to this direction.

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And so in this
case here, you have

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a particle and an antiparticle
unrelating to a photon.

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So far, so good so.

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This is again a good
point to stop and just

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try to read the diagrams.

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Note that what happens in this
discussion when you actually

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change the direction of time--

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forward down.

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You want either directions.

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So now if you want to
calculate the reaction,

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it's not sufficient to
just use one word vertex.

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Why?

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Because a single vertex will not
be able to give us a reaction.

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You can simply see
this when you look

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at something like an electron
plus electron photon.

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This is not really possible
because of energy and momentum

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conservation in this diagram.

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So you need a couple of vertices
in order to make a reaction.

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So this here is, again,
we have potentially

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the time going this direction.

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There's a scattering between
an electron and a muon

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through the exchange
of a photon.

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Both particles have
electric charge of e.

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And then you can
just calculate what

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is the probability for a
process like this to occur.

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We'll see how to do this
technically later on.

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But hopefully you have
a first impression.

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Again, let's label
this now very quickly.

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So you have an
incoming particle,

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a second incoming particle,
outgoing particles,

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and an exchange particle.

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So this exchange
particle is a photon.

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And there's two vertices
in this diagram.