Hello! Im currently reading Ryder's QFT book and am confused with the variation of a scalarfield. He writes that the variation can be done in two ways, [tex] \phi(x) \rightarrow \phi'(x) = \phi(x) + \delta \phi(x) [/tex] and [tex] x^\mu \rightarrow x'^\mu = x^\mu + \delta x^\mu. [/tex] This seems reasonable. But later, in order to proceed with Noether's theorem he states that the variation is of the form (eq 3.22): [tex] \Delta x^\mu = X^\mu_\nu \Delta \omega^\nu, [/tex] and [tex] \Delta \phi = \Phi_\mu \delta \omega^\mu. [/tex] I dont know how to interpret this. What is a function over spacetime? Is 'X' our generators for the group of transformations? If someone feels like expanding on this transformation I would be very happy. I can see that we are describing the total variation in the last equations but why dont we just vary the scalarfield with another scalar function? It seems to just complicate things this way. :( Thanks for your time guys and girls!