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[CLICKING]

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MARKUS KLUTE: Welcome
back to 8.701.

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So in this second chapter--

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chapter number 1-- we
start talking about

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quarks' and leptons'
interactions and fields.

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And we start by a very
general discussion

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of quantum fields and matter.

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So you all know what we
mean by particles and forces

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in the classical sense.

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However, we need now to see
how they connect with quantum

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fields, and how this helps us
to consider matter and forces

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in a very similar way.

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The modern view of the basic
way that particles come to exist

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is in terms of
quantized fields, which

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is an extension of the quantum
mechanics you love and know,

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which you have done before,
where you quantize particles.

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These fields have quantum
equations for their field

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amplitudes which are
basically like the quantum

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simple harmonic
oscillator, but there are

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an infinite number of them--

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one for every possible
frequency of wave in the field.

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This means the amplitudes for
the wave for each frequency

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are therefore quantized
in integer steps,

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just like in a simple
harmonic oscillator.

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This is what we
see as a particle.

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The first excitation gives
one particle of a frequency.

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The further excitation
of the amplitude

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for the same frequency
corresponds to two particles.

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Et cetera, et cetera.

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So hence, the concept
of quantum field,

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unlike normal quantum
mechanics, allows

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an arbitrary and changeable
number of particles to exist.

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This is necessary, as
you will see later,

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such that we can create
and annihilate particles

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in reactions and decays.

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And the standard
wavefunctions correspond

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to an equation of a
particular frequency,

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amplitude when it exists
in the [INAUDIBLE]..

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So now, just let's
consider a few cases here.

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Imagine you have two particles--
two fermions, for example--

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let's say two electrons.

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And you consider
the wavefunction.

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Quantum field
theory actually says

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that there's only
one electron quantum

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field for the whole universe,
and every electron which exists

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is due to an excitation
of the field.

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Hence, all electrons
are identical

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in the quantum-mechanical
sense, as they all

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arise from the same field.

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The theory says, then, that
particular properties are

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the resulting wave equations--
namely, their symmetry--

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and the exchange
of these particles.

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So the extra symmetry
depends on whether or not

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the particle is a fermion,
which means it has spin 1/2

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or 3/2 or 5/2, et cetera, or a
boson, which means that it has

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spin 0, 1, or 2, and so on.

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So for any identical
fermion and electron,

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our quantum field theory
says that their wavefunction

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must obey the property
of antisymmetry.

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This means that when we
write an overall wavefunction

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and we replace the particles,
we pick up a minus sign.

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This property is not
just for electrons,

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but for all fermions--

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that's all matter particle,
as we saw last week.

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So it also holds for
composite particles.

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A composite spin-1/2 particle
is subject to the same

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antisymmetry.

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This property of exchange
antisymmetry leads

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to a well-known principle--
namely, the Pauli principle,

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which means that you cannot
have two electrons of the same

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energy state or the same state,
because when you would actually

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swap them, you find
that they are identical,

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which is a stark contrast to
the actual description of this

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wavefunction.

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So this doesn't really work.

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And therefore, two
electrons, or two fermions,

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cannot be in the same state.

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[INAUDIBLE] very general.

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Constructing a wavefunction or
a total wave equation for two

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fermions is not that hard.

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We can simply do this
by this construction.

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An important additional
statement or note to take here

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is that an antiparticle
such as a positron

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is not identical to a particle,
such as to the electron, again.

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If you move on to bosons,
boson exchange is symmetric,

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meaning that if you
[? request ?] two photons,

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you find the identical
wavefunction.

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And then constructing a
two-boson total wavefunction,

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you do this by adding those
two functions together.

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This is, by
definition, symmetric.

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Let's look now forward
to exchange particles.

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Again, you have a very good
idea of the classical picture

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of how forces are transmitted.

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So the modern picture of how a
force acts under quantization

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is by emission and by
absorption of a particle.

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That is shown in
this diagram here,

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where let's say you have an
electron and a second electron.

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They see each other.

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And they see each other by
emitting and absorbing photons.

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And you see this here.

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So this electron comes along,
maybe emitting a photon.

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This electron [? readmits ?] it.

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And by this exchange of
emission and absorption

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of photon, those two
particles, the [INAUDIBLE]

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electrons to each other.

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So this you can think about
like two ships shooting cannons,

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if you want.

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But you also have to consider
that there is not just

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repelling forces, but
also attracting forces.

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We could have replaced the
electron with a positron,

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and the negative and
the positive charge

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would interact with each other.

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This is it for this short--

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it's basically an intro
into the intro of the intro.

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I hope you enjoy this.

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All of those concept
we go into more detail.

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This is really just
the starting point.

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And then the next
lecture, you'll

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see how we can
actually understand

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aspects of this
diagram here, which

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we call the Feynman diagram.