I'm having difficulty deciphering my notes which 'proove' that the commutor of two real free fields φ(x) and φ(y) (lets call it i∆) ie. i∆=[φ(x),φ(y)] are Lorentz invariant under an orthocronous Lorentz transformation. Not sure if it helps but φ(x)=∫d3k[α(k)e-ikx+α+(k)eikx]. Now, apparently I have to 'observe' that: i∆=∫d4k.δ(k2-m2)ε(k0)e-ikx where ε(k0) = 1 if k0>0 and -1 if k0<0. Firstly, I can't see at all, how this expression comes about: why there is a delta function δ(k2-m2) (this looks like the mass shell condition, but why is it relavent here?) The "ε(k0) keeps positive k0 positive and negative k0 negative". I guess this makes sense because an orthocronous LT maps future directed vectors to future directed vector and past to past. But I still can't see why that expression proves that ∆(Lx)=∆(x). Any thought?