I) Non Abelian Gauge

Question 1

Given an arbitrary gauge potential the polarization vector has 4 components, though light only has 2 polarizations. What two equations reduced the degrees of freedom of the polarization?

Answer 1

1. Partial derivative of field strength = 0 (From here epsilon*k=0 iff k^2=0, otherwise EM-field=0)
2. The same equation for a gauge transformation

Question 2

What happens to the field vector and the field wavefunction under minimal coupling?

Answer 2

A_mu –> A_mu - partial_mu Chi

Psi –> e^(iqChi)Psi

Question 3

What two ingredients couple the EM-field to matter?

Answer 3

Minimal couling and the covariant derivative

Question 4

What is the free Dirac equation based on?

Answer 4

Minimal coupling and the free Schrödinger equation

Question 5

Why are there 8 gluons?

Answer 5

Because dim SU(n) = n^2-1 and n=3 for gluons

Question 6

The Pauli matrices are the generators of…

Answer 6

SU(2)

Question 7

The Gell-Mann matrices are the generators of…

Answer 7

SU(3)

Question 8

What is the definition of the adjoint representation?

Answer 8

dim(Adj)=dim(G)

Question 9

What three ingredients generalise QED to SM?

Answer 9

1. Non-abelian gauge symmetry
2. Chiral fermions
3. Spontaneous symmetry breaking