1. The inclusion of fermions – J=1/2 particles
Weyl spinors
Dirac spinor
2-component spinors of SU(2)
velocity
Left-handed
m=0
Right-handed
The spinor structure follows from the representation structure of the Lorentz Group …

2. The Lorentz transformations form a group, G
Rotations
Angular momentum
operator

3. } } The Lorentz group Generate the group SO(3,1)
To construct representations a more convenient (non-Hermitian) basis is }

4. } The Lorentz group Generate the group SO(3,1)
To construct representations a more convenient (non-Hermitian) basis is
Representations

5. Weyl spinors Dirac spinor 2-component spinors of SU(2)
Rotations and Boosts
Dirac spinor
Can combine
to form a 4-component “Dirac” spinor
Lorentz transformations
where
Weyl basis

6. Weyl spinors Dirac spinor 2-component spinors of SU(2)
Rotations and Boosts
Dirac spinor
Can combine
to form a 4-component “Dirac” spinor
Lorentz transformations
where
(Dirac gamma matrices, …new 4-vector )
Note :

7. The Dirac equation Fermions described by 4-cpt Dirac spinors
Lorentz invariant
New 4-vector
The Lagrangian
Dimension?
From Euler Lagrange equation obtain the Dirac equation
Feynman rules
U(1) symmetry

8. Fermion masses Lorentz invariant Dirac mass Lorentz invariant
Only term allowed by charge conservation is
Majorana mass

9. Fermions and the weak interactions
Fermi theory of decay

10. } V-A Fermions and the weak interactions Fermi theory of decay W+ p n

11. Weak Interactions Symmetry : Local conservation of
SU(2) local gauge theory
Symmetry :
Local conservation of
2 weak isospin charges
Weak coupling, α2 u d
Gauge boson
(J=1)
Wa=1..3
A non-Abelian (SU(2))
local gauge field theory e
Neutral currents

12. Massive vector propagator (W, Z bosons)
Free particle solution
Helicity polarisation vectors

13. } Propagation of unstable scalar particle No decay iJ iJ ..
Particle decays
into final state n …. iJ
Optical theorem – conservation of probability, time evolution is unitary }

16. Fermi theory (‘40s)
Dimensional analysis
The hard part!

17. In μ decay

20. Have Fun! Fundamental principles of particle physics
Introduction - Fundamental particles and interactions
Symmetries I - Relativity
Quantum field theory - Quantum Mechanics + relativity
Theory confronts experiment - Cross sections and decay rates
Symmetries II – Gauge symmetries, the Standard Model
Fermions and the weak interactions
The Standard Model and Beyond
Have Fun!

22. velocity
Left-handed
m=0
Right-handed