I just received by mail the book by Weinberg
I am very very happy. At each page I can see something new to learn.
But I would like to learn a bit more about his remark on page 28.
(you can read it with the amazon reader)
He talks about the 10 parameter Poincaré group, that I knew already.
But he also mentions a 15-parameter group called "conformal group".
He explains this is the group of transformations that leave invariant the ds²=0 condition (the ds² is not necessarily invariant, only the condition ds² is).
I would learn to much more about that.
For example, Weinberg excludes this group as a valid symmetry in physics, but the explanation is not totally clear for me.
Also, why are there 15 parameters in this group?
Also, what do these transformation look like?
Also, when I read Landau-Lifchitz, I read arguments explaining that in any symmetry tranformation we should have ds²=A(V)ds'² and that A(V) should be a constant to satisfy the hypothesis of space homogeneity. I did not care too much at that time. But now, with this new reading in Weinberg, I need to understand more and see the missing link.
Thanks for your impetus ...