This is a problem from my theoretical physics course. We were given a solution sheet, but it doesn't go into a lot of detail, so I was hoping for some clarification on how some of the answers are derived. 1. The problem statement, all variables and given/known data For the Lagrangian L=1/2(∂μ∅T∂μ∅-m2∅T∅) derive the Noether currents and charges. 2. Relevant equations jμa=∂L/(∂(∂μ∅a))*[itex]\Phi[/itex]aα - [itex]\Lambda[/itex][itex]\mu[/itex]α Here, the lambda term is zero, because the Lagrangian is invariant under SO(3). ∅a → ∅a + [itex]\Phi[/itex]aαεα 3. The attempt at a solution We were first told to show that the above Lagrangian satisfies SO(3) symmetry (this was fine). The solution sheet then states that infintessimal transformations can be written as ∅a → ∅a-itc(Tc)ab∅b, where (Tc)ab=-iεcab I could not work out how to derive this though. Using the above info, I can see that [itex]\Phi[/itex]ac = -i(Tc)ab∅b, taking εα = tc Then I just need to calculate ∂L/∂(∂μ∅a) Is this just ∂μ∅a?? I'm not sure how to calculate this when there's 2 derivatives, one with a superscript and one with a subscript. And does the transpose affect things?