Recently, I read some books and articles about conformal field theory and I find there exists two completely different views about conformal transformation...
The first is that: Conformal transformation is a special coordinate transformation, or diffeomorphism, that leaves the metric invariant up to a scale change.
Francesco's Conformal Field Theory hold that view, as well as some other references such as "Applied Conformal Field Theory" by Ginsparg: http://arxiv.org/abs/hep-th/9108028
And the second one is that: Conformal transformation is only a rescale of metric and we do not transform coordinate. It can be done by a diffeomorphism followed by undoing the associated metric transformation or undoing the associated coordinate transformation.And it seems to be exactly a Weyl transformation.
Wald hold this view in his book "General Relativity". And he said a CT is not, in general, associated with a diffeomorphism.
And I get confused. Which one is correct....I can not bear it that a basic concept have two completely different, even contradictory interpretation... Or they are just my misunderstanding?
