Contents
1
Introduction
2
Symmetries in physics
3
Quantum field theory
4
The Standard Model
Bibliography
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Contents
1
Introduction
2
Symmetries in physics
2.1
Rapid review of group theory
2.1.1
Group representations
2.1.2
Continuous symmetries
2.2
Lie algebras
2.2.1
The fundamental and adjoint representations
2.2.2
General representations
2.3
Particles are irreps of the Poincaré group
2.3.1
The Lorentz group
2.3.2
The Poincaré group
3
Quantum field theory
3.1
Classical field theory
3.1.1
Lagrangian mechanics
3.1.2
Free scalar field theory
3.1.3
Symmetries and Noether’s theorem
3.1.4
Hamiltonian mechanics
3.2
Quantization
3.2.1
Canonical quantization
3.2.2
The Hamiltonian and the vacuum catastrophe
3.2.3
Particles
3.2.4
The complex scalar field and antiparticles
3.2.5
Propagators and Green functions
3.3
Interactions
3.3.1
Interactions in the Lagrangian
3.3.2
S-matrix elements
3.3.3
Feynman diagrams
3.3.4
Decay rates and cross sections
3.4
Spinor field theory
3.4.1
The Dirac equation
3.4.2
Spinors
3.4.3
The Dirac Lagrangian
3.4.4
Quantizing the Dirac field
3.4.5
Interactions and Feynman rules
3.4.6
CPT Symmetries
3.5
Gauge theories
3.5.1
Why gauge invariance?
3.5.2
Maxwell Theory
3.5.3
Quantum electrodynamics
3.5.4
Yang-Mills Theory
3.5.5
Quantized Yang-Mills Theory
3.5.6
Running coupling and asymptotic freedom
3.6
The ABEGHHK (Higgs) mechanism
3.6.1
The abelian Higgs mechanism
3.6.2
The non-abelian Higgs mechanism
4
The Standard Model
4.1
Quantum chromodynamics
4.1.1
Asymptotic freedom and confinement
4.1.2
Quarks and the eightfold way
4.1.3
The parton model
4.1.4
Jets
4.2
Electroweak interactions
4.2.1
Weak interactions
4.2.2
Before electroweak symmetry breaking
4.2.3
Electroweak symmetry breaking
4.2.4
Fermion masses and flavor
4.3
Beyond the Standard Model [Coming Soon!]
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