A. Zee, Quantum Field Theory in a Nutshell · Problem VII.1.2

Field Theory Redux

Physics — QFT

Problem

Derive (17) and relate

f

to the coupling

g

in the continuum formulation of Yang-Mills theory. [Hint: Use the Baker-Campbell-Hausdorff formula

e^A e^B = e^{A+B+\frac{1}{2}[A,B]+\frac{1}{12}([A,[A,B]]+[B,[B,A]])+\cdots}

]