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Introduction to the Standard Model
----------------------------------
Overview
--------
The Standard Model of particle physics is a theory concerning
the electromagnetic, weak, and strong nuclear interactions, as
well as classifying all known subatomic particles.
The Standard Model includes 12 elementary particles of spin 1/2.
There are 6 quarks and 6 leptons. Pairs from each classification
are grouped together to form a generation, with corresponding
particles exhibiting similar physical behavior.
Every particle shown has an antiparticle associated with it.
Gluons, the photon, the Z and the Higgs boson are their own
antiparticle. The W^{+} boson is the antiparticle of
the The W^{-} boson.
The mathematics of the elementary particles is grounded in
symmetries described by Special Unitary groups and Lie algebras.
Quantum Flavordynamics
----------------------
Quantum Flavordynamics involves the transition of the up quark
to the down quark and the electron to the neutrino and vice versa.
The generators of SU(2) are the Pauli matrices that also describe
spin angular momentum. The conserved quantity is the weak isospin
(weak isospin has nothing to do with spin - just the same math!).
This is apparent when considering the decay of a neutron to a
proton.
_
udd -> uud + e + ν_{e}
Electroweak Unification
-----------------------
Electroweak unification is described by SU(2)_{L} ⊗ U(1)_{Y}.
The generator of U(1)_{Y} is the weak hypercharge defined as.
Y_{W} = 2(Q - I_{3})
Note: U(1)_{Y} is different to the U(1)_{em} in QED whose generator
and conserved quantity is the electric charge, Q, derived from
Noether't theorem.
Quantum Chromodynamics
----------------------
Quantum Chromodynamics involves the transitions between the
3 quark colors and is described by SU(3). The generators of
SU(3) are the Gell-Mann matrices and the conserved quantity
is the color charge.
The Gell-Mann matrices generalize the Pauli matrices for SU(2)
and SU(3) contains SU(2) weak isospin as a subgroup.
Gauge Bosons
------------
In the Standard Model, gauge bosons are defined as force
carriers that mediate the strong, weak, and electromagnetic
fundamental interactions. Transitions between states occur
as a result of these interactions. To describes interactions
it is necessary to invoke Quantum Field Theory and Lagrangian
mechanics. The Lagrangian controls the kinematics of the
theory. Each kind of particle is described in terms of a
dynamical field that pervades spacetime. The basic idea is
to introduce gauge fields into the Lagrangians which make
them invariant under local symmetry transformations. The
gauge bosons are the quanta of these fields. The mathematics
of gauge invariance is based on Yang-Mills theory.
The Standard Model is a non-abelian gauge theory with the
symmetry group U(1)×SU(2)×SU(3) and has a total of 12 gauge
bosons: the photon, 3 weak bosons and 8 gluons.
Higgs Mechanism
---------------
The Standard Model has been enormously successful in explaining
a wide variety of experimental results but until recently could
not explain why particles have mass. This riddle was finally
solved with the verification of the Higgs mechanism in 2013.
The Higgs mechanism postulated that particles gain mass as a
result of spontaneously symmetry breaking brought about by the
presence of a Higgs Field that permeates the Universe.