Fundamental principles of particle physics

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Fundamental principles of particle physics
Our description of the fundamental interactions
and particles rests on two fundamental
structures
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Symmetries
Central to our description of the fundamental
forces
Relativity - translations and Lorentz
transformations
Lie symmetries -
Copernican principle Your system of
co-ordinates and units is nothing special
Physics independent of system choice
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Fundamental principles of particle physics


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Special relativity
Space time point
not invariant under translations
Space-time vector
Invariant under translations but not invariant
under rotations or boosts
Einstein postulate the real invariant distance
is
Physics invariant under all transformations that
leave all such distances invariant
Translations and Lorentz transformations
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Lorentz transformations
(Summation assumed)
Solutions
3 rotations R
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Lorentz transformations
(Summation assumed)
Solutions
3 boosts B
3 rotations R
Space reflection parity P
Time reflection, time reversal T
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The Lorentz transformations form a group, G
Rotations
Angular momentum operator
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The Lorentz transformations form a group, G
Rotations
Angular momentum operator
The
are the generators of the group.
Their commutation relations define a Lie
algebra.
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Demonstration that
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Derivation of the commutation relations of SO(3)
(SU(2))
Equating the two equations implies
QED
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Fundamental principles of particle physics


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Relativistic quantum field theory
Fundamental division of physicists world
Action, S
speed
slow
fast
Ac t ion
Classical Newton
Classical relativity
large
Classical Quantum mechanics
Quantum Field theory
small
Principle of Least Action Feynman Lectures in
Physics Vol II Chapter 19
c
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Relativistic quantum field theory
Fundamental division of physicists world
speed
slow
fast
Ac t ion
Classical Newton
Classical relativity
large
Classical Quantum mechanics
Quantum Field theory
small
c
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Quantum Mechanics Quantization of dynamical
system of particles
Quantum Field Theory Application of QM to
dynamical system of fields
Why fields?
No right to assume that any relativistic process
can be explained by single particle since Emc2
allows pair creation
(Relativistic) QM has physical problems. For
example it violates causality
Amplitude for free propagation from x0 to x
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Quantum Mechanics
Classical non relativistic
Quantum Mechanical Schrodinger eq
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Quantum Mechanics
Classical non relativistic
Quantum Mechanical Schrodinger eq
Classical relativistic
Quantum Mechanical - relativistic
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Relativistic QM - The Klein Gordon equation (1926)
Scalar particle (field) (J0)
(natural units)
Energy eigenvalues
1927 Dirac tried to eliminate negative solutions
by writing a relativistic equation linear in E
(a theory of fermions)
1934 Pauli and Weisskopf revived KG equation with
Elt0 solutions as Egt0 solutions for particles of
opposite charge (antiparticles). Unlike Diracs
hole theory this interpretation is applicable
to bosons (integer spin) as well as to fermions
(half integer spin).
As we shall see the antiparticle states make the
field theory causal
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