# Electroweak Theory

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```					Electroweak Theory

Mr. Gabriel Pendas
Dr. Susan Blessing
The Standard Model
 The Standard Model describes our current
view of particle physics incorporating the
leptons, hadrons, and bosons (the force
carriers)
 The four forces in the standard model are:
 Strong  – force between quarks in nuclei
 Electromagnetic
 Weak
 Gravity – weakest force; between very large
objects
Electromagnetic Force
 It has an infinite range!
 Its has a relative strength to the strong
force of 10^-2 if the strong force is give a
strength of one
 Its mediator particle is the photon
 It is what’s responsible for making sure
you don’t fall through the ground
Quantum Electrodynamics
 Quantum theory of the interaction of
charged particles with the electromagnetic
field
 Rests on the idea that the charged
particles interact by emitting and
absorbing photons, the particles of light
that transmit the electromagnetic force
 QED is both renormalizable and gauge
invariant
Renormalization
   In QED when you have a virtual photon electron-
positron pairs may be created with as high energy or
momentum as can be allowed
   These are quantum fluctuations because energy and
momentum are not conserved locally
   This creates infinities when doing any type of physical
calculation, the most well known being cross-sections
   You use the technique of renormalization which sort of
sweeps these inifinities under the rug and is explained
further in Quantum Field Theory A
   Seriously, it’s a very advanced mathematical technique
that is beyond the scope of this talk
Gauge Invariance
 Physics has many globally invariant quantities like space,
time, voltage, etc…
 Can quantities be locally invariant as well?
 Yes, begin with the Schrodinger equation of a particle
moving in empty space, and introduce a complex phase
 You will find that the probability of finding a particle in a
state does not change even if we introduce a different
complex phase at different points in space as long as we
introduce a modification to our vector potential known as
a gauge transformation
 The gauge transformation requires the introduction of
additional fields known as gauge fields.
 The quantization of these fields produces the gauge
boson
Gauge Invariance (cont.)
 In the electromagnetic case our vector potential
can be interpreted as the electromagnetic vector
potential which leads to the introduction of the
magnetic and electric field
 Electromagnetic gauge invariance is a local
symmetry called a U(1) gauge symmetry
 The gauge boson for the electromagnetic force
is the photon
Search for a Weak Theory
 So a quantum theory of the weak theory
must be two things, it must be gauge
invariant and its must be renormalizable
 Gauge invariance requires that the boson
which carries the force be massless, which
is okay in E&M but the weak force is short
range which would imply that its boson
would have mass
Symmetries
 Physicists were trying to come up with numerous models
that were symmetric to explain the weak force, this is
the method Weinberg used when he introduced the
symmetry for his and Salaams electroweak theory
 If we look at leptons, there are two left-handed electron
type leptons and one right handed electron type so we
can start with the group U(2) x U(1)
 Breaking up U(2) into unimodular transformations and
phase transformations, one could say the group was
SU(2)x U(1)x U(1)
 But, since one of the U(1)s can be identified with lepton
number and lepton number is conserved our new
symmetry is SU(2) x U(1)
Symmetry Breaking
 If this new symmetry is to uphold then all four
particles must be massless, but the weak force
is a short range force not an infinite one so its
boson must have mass
 The symmetry must be broken so the Higgs
mechanism was introduced.
 When a particle interacts with a Higgs potential
they might begin at the origin at the maximum
which will still conserve symmetry however the
Higgs field pushes the particle to the minimum
and symmetry is broken!
Symmetry Breaking (cont.)
 In our case the SU(2)xU(1)is broken to the U(1)
symmetry of ordinary electromagnetic gauge
invariance.
 Since we have four parameters or rather four
particles this symmetry breaking would allow
three of our four particles to have mass.
 These four particles were found found to be our
three weak bosons the, W+, W- and Z, and the
massless particle that was left over is the photon
of the electromagnetic force
 Therefore, we had a unified theory of
electroweak interactions
Weak Theory (cont.)
 So we have shown how we can have massive bosons
with gauge invariance, what about renormalization?
 This wasn’t done till later by ‘t Hooft and Veltman who in
1971 introduced dimensional regularization which put
the second to final nail in the coffin for electroweak
theory and won them the Nobel prize in 1999.
 The final nail in the coffin was made by the discovery of
the W and Z bosons in 1983 by Carlo Rubbia and Simon
Van der Meer which won them the Nobel prize in 1984.
 For their contributions in the construction of the
electroweak theory Weinberg, Salaam, and Glashow won
the Nobel Prize in 1979.

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