I am reading my textbook of QFT (Maggiore, Modern Introduction in QFT), and there is this statement:(adsbygoogle = window.adsbygoogle || []).push({});

"If [itex] T^a_R [/itex] is a representation of the algebra and V a unitary matrix of the same dimension as [itex] T^a_R [/itex] , then [itex] V T^a_R V^\dagger [/itex] is still a solution o the Lie algebra and therefore provides an equivalent representation. We can fix V requiring that it diagonalizes the matrix [itex] D^{ab}(R) ≡ Tr (T^a_R T^b_R) [/itex], so that [itex] Tr (T^a_R T^b_R) = C(R) \delta^{ab} [/itex]."

I can't understand the second sentence, matrix D has different dimensions than V, how can it be used to diagonalize? Putting V within the trace doesn't make any sense, it would give unit matrix.

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Normalization of SU(N) group

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**