Srednicki — Quantum Field Theory · Problem 81.4

Canonical Quantization of Scalar Fields — Mark Srednicki

Physics — QFT · scattering-qcd

Problem

a) Verify eqs. (81.58) and (81.59) using the double-line notation of section 80. b) Compute

\mathrm{Tr}(T^a_R T^b_R T^b_R T^a_R)

and

\mathrm{Tr}(T^a_R T^b_R T^a_R T^b_R)

in terms of the index

T(R)

and dimension

D(R)

of the representation

R

, and the index

T(A)

and dimension

D(A)

of the adjoint representation. Verify that your results reproduce eqs. (81.58) and (81.59).