A. Zee, Quantum Field Theory in a Nutshell · Problem VII.4.1

Field Theory Redux

Physics — QFT

Problem

Since the number of gluons only differs by one, it is generally argued that it does not make any difference whether we choose to study the

U(N)

theory or the

SU(N)

theory. Discuss how the gluon propagator in a

U(N)

theory differs from the gluon propagator in an

SU(N)

theory and decide which one is easier.