IV) Construct the Standard Model

Question 1

The fields in the SM are quantum fields (and not classical fields). What does that mean?

Answer 1

They are operators (acting on ket-states). It follows from this that they do not commute, in general.

Question 2

The combined groups SU(2)_L

×U(1)_Y describe what symmetry?

Answer 2

Electroweak symmetry

Question 3

What are the fields in the standard model?

Answer 3

• Fermion field (for matter)
• Electroweak field (for charge and isospin)
• Gluon field (for color)
• Higgs field (for scalar potential)

Question 4

What is the defining principle of Fermi-Dirac statistics?

Answer 4

The Pauli exclusion principle. This is because fermionic fields obey canonic anticommutation relations.

Question 5

Why are there no fermion mass terms in the SM Lagrangian?

Answer 5

Because of chirality and gauge invariance.

Question 6

What is Yang-Mills theory?

Answer 6

A gauge theory of SU(n), n>1. They are non-abelian and the Lagrangian is only the Maxwell term.

Question 7

What is the charge of SU(3), SU(2), and U(1) respectively?

Answer 7

color (C), weak isospinn (T^3), and hypercharge (Y)

Question 8

What is the Gell-Mann–Nishijima formula?

Answer 8

Q=T^3+(1/2)Y

Question 9

What interactions can change flavor?

Answer 9

Only weak interactions with the W-boson.