A. Zee, Quantum Field Theory in a Nutshell · Problem VII.5.3

Field Theory Redux

Physics — QFT

Problem

Check that the

SU(3) \otimes SU(2) \otimes U(1)

theory is anomaly-free. [Hint: The calculation is more involved than in

SU(5)

since there are more independent generators. First show that you only have to evaluate

\text{tr} Y \{T_a, T_b\}

and

\text{tr} Y^3

, with

T_a

and

Y

the generators of

SU(2)

and

U(1)

, respectively.]