Questions after Lecture 2
The Standard Model
Control Questions
- Why is the Standard Model better viewed as a quantum-field-theory Lagrangian than as a particle table?
- What is the phase-convention problem in the “three friends” story?
- Why is the free Dirac Lagrangian not invariant under a local phase transformation?
- How does introducing (A_) and replacing () by (D) make QED possible?
- Why does gauge invariance forbid a photon mass term (m_A^2A_A^)?
- In what ways do electromagnetic and weak interactions look different before unification?
- What are the two pillars needed after choosing the group (SU(2)_LU(1)_Y)?
- What does neutron decay illustrate about weak interactions in the Standard Model?
Additional Questions
- How does the gauge principle turn a symmetry of the free theory into an interaction?
- What is the analogy between the Meissner effect and mass generation for a vector boson?
- How does the Higgs condensate couple right- and left-moving chiral fermion waves?
- Why do Yukawa couplings parameterize fermion masses but not explain their hierarchy?
- What does the finite condensate layer animation show about transmission, reflection, and reduced group velocity?
- What does it mean to say that the Standard Model is a consistency machine?
Short Exercise
Using the estimate from the lecture,
\[ R\sim \frac{1}{M_W}, \qquad 1\ \mathrm{GeV}^{-1}=0.197\ \mathrm{fm}, \]
estimate the range of the weak interaction for (M_W ). Compare the answer with an atomic scale of order (10^{-10} ).