Srednicki — Quantum Field Theory · Problem 70.3

Canonical Quantization of Scalar Fields — Mark Srednicki

Physics — QFT · index-adjoint-representation-son

Problem

a) Consider the

\mathrm{SO}(3)

subgroup of

\mathrm{SO}(N)

that acts on the first three components of the fundamental representation of

\mathrm{SO}(N)

. Under this

\mathrm{SO}(3)

subgroup, the N of

\mathrm{SO}(N)

transforms as

3 \oplus (N-3)

1's. Using eq. (70.29), figure out how the adjoint representation of

\mathrm{SO}(N)

transforms under this

\mathrm{SO}(3)

subgroup. b) Use your results from part (a) and from problem 70.2 to compute

T(\mathrm{A})

for

\mathrm{SO}(N)