# How to find the generator of translation?

by kakarukeys
Tags: generator, translation
 P: 190 The Galilei group contains rotations, Galilean transformations, space translation and time translation. It is easy to work out generators for rotations and Galilean transfromations in matrix form. And they obey: $$[J^i, K^j] = i \epsilon^{ijk}K^k$$ Can one work out the generator for space translation, $$P$$? so that one can show explicitly that: $$[K^i, P^j] = 0$$ and same for time translation. $$[K^i, H] = i P^i$$ OR there is no matrix form for these two generators?
 P: 599 Isn't the generator for space translations $$e^{i \hat{p}a/\hbar}$$? Or is a generator something different?
 P: 190 How to find the generator of translation? I do not quite understand what you said. But I found the answer. The matrix can be found by expanding the 4D space to 5D, provided that $$x_5$$ is always 1.