- #36
latentcorpse
- 1,444
- 0
fzero said:Write down an expression for [tex]\dot{Q}_a[/tex] in terms of [tex] j_{a0}[/tex] and use [tex]\partial^\mu j_{a\mu}=0[/tex] to show that it vanishes. It's kind of simple, I'm not sure what else I could say without giving it completely away.
ok so we had [itex]Q_a = - \frac{1}{2} \int j_a{}^0[/itex]
i notice you have the 0 index "down" - is this important?
anyway [itex]\dot{Q_a} = - \frac{1}{2} \int \partial_0 j_a{}^0[/itex] (where i hope my indices are correct since i want to contract over the 0 index and [itex]\partial_0 = \frac{\partial}{\partial t}[/itex]
but [itex]\partial_\mu j_a{}^\mu = 0 \Rightarrow \partial_0 j_a{}^0 = - \partial_i j_a{}^i[/itex]
giving [itex]\dot{Q_a} = \frac{1}{2} \int \partial_i j_a{}^i[/itex]
how does that go to 0 though?