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Symmetry Methods in Physics
·
Module 10
Gauge Theories and Fundamental Symmetries
1
Constructing SU(N) Yang-Mills Theory
Construct a non-abelian gauge theory (Yang-Mills theory) from the principle of local SU(N) gauge invariance.
2
Yang-Mills Theory: Field Strength Tensor and Lagrangian
Derive the non-abelian field strength tensor and the gauge-invariant Yang-Mills Lagrangian.
3
Gauge Fixing and Faddeev-Popov Ghosts in Non-Abelian Quantization
Describe the role of gauge fixing and Faddeev-Popov ghosts in the quantization of non-abelian gauge theories.
4
Standard Model Gauge Group
Identify the gauge group structure of the Standard Model as SU(3)xSU(2)xU(1).
5
Parity and Charge Conjugation of Dirac Fields
Define the parity (P) and charge conjugation (C) transformations and their action on Dirac fields.
6
Time Reversal and Anti-Unitarity in QFT
Define the time reversal (T) transformation and explain its anti-unitary nature in quantum field theory.
7
CPT Theorem and Particle-Antiparticle Properties
State the CPT theorem and describe its implications for particle-antiparticle properties.
8
Chiral Symmetry and the Chiral Anomaly
Define chiral symmetry for massless Dirac fermions and describe the chiral anomaly as a quantum-mechanical breaking of a classical symmetry.
Previous module
Noether's Theorem and Gauge Symmetries
Next module
Spontaneous Symmetry Breaking