## Physics 7314 and 7315

## Syllabus

### Learning Outcomes

- On completion of this course, students will be able to construct relativistic
quantum field theories, and use them to compute predictions such as cross sections
and decay rates. In particular, they will be able to identify the ingredients in the
gauge theories that make up the Standard Model of particle physics. After the first
course, they can discuss the general properties of known particles and the scales of
their interactions, explain the role of symmetries in constructing actions, and apply
these to scalar fields. In the subsequent course, they will be able to compute
tree-level decay rates and cross sections for model scalar theories, and for the
gauge theories of the standard model. They will also be able to discuss the
complexities involved in one-loop and higher calculations. They will be able to
categorize fields and states as representaions of both the Lorentz group and of the
nonabelian groups SU2 and SU3. Finally, they will be able to explain mass generation
via the Higgs mechanism.
Students will demonstrate their understanding by completing assigned problems.

### Topics

- Introduction I - Units and Scales
- Introduction II - Basics of Particles and Interactions
- Klein-Gordon and Dirac Relativistic Quantum Mechanics
- Rotational and Lorentz Symmetry
- Scalar Field I - Intro
- Scalar Field II - Symmetry and Conservation
- Scalar Field III - Particles
- Antiparticles and Causality
- Particle Exchange and Potentials
- Interaction Picture and S matrix
- ABC Model Decay
- Scattering Cross Sections (General)
- AB to AB Scattering
- Resonances
- Groups and Representations
- Lorentz Group and Spinors
- Dirac Spinors and the Dirac Equation
- Quantum Electrodynamics and Gauge Symmetry
- QED Processes
- Deep Inelastic Scattering and Partons
- Loops and Renormalization
- Running Couplings and Masses
- Weak Interactions
- Vector Bosons
- Symmetries and the Vacuum
- Goldstone Bosons
- Higgs Mechanism
- Non-Abelian Gauge Field Lagrangians
- Higgs Mechanism in SU(2)xU(1)
- Quantum Chromodynamics
- Path Integrals and Lattice QCD

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