6. Spontaneous Symmetry Breaking and the Higgs

Question 1

What does it mean if a theory is “renormalizable”?

Answer 1

Can systematically remove the infinities in the loop diagrams leaving finite predictions

Question 2

What is the Higgs field and explain what it does to the SU(2) gauge symmetry

Answer 2

The Higgs field couples to both gauge bosons and fermions
- Its properties break the SU(2) gauge symmetry spontaneously, giving mass to all the elementary particles

Question 3

What are the two methods to break a symmetry?

Answer 3

Explicitly and spontaneously

Question 4

Describe what explicitly breaking the symmetry means

Answer 4

You have some part of the Lagrangian which is not invariant under the symmetry so is broken

Question 5

Describe what spontaneously breaking the symmetry means

Answer 5

The Lagrangian is symmetric wrt the symmetry, but the ground state of the theory is not invariant
- The ground state breaks the symmetry, not the Lagrangian like in the explicit case

Question 6

What is the principle of least action?

Answer 6

Minimise the action wrt the trajectories of position and motion and you find the equation of motion of the system

Question 7

What group are all right handed fields?

Answer 7

SU(2) singlets

Question 8

How do Gauge couplings couple to the left and right handed states?

Answer 8

They couple LH to LH or RH to RH