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comment Is there a natural (suitable) definition for functional derivative in Curved space time
Thanks for your answer. The extra terms 'derivative over g' , in the case of functional derivative by g_{\mu \nu} will give -1/2 \sqrt{g} g^{\mu \nu} \delta g_{\mu \nu} so you see I can again extract out the \sqrt{g}. Do you think this prescription have the chance of commutativity?
Jun
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comment Is there a natural (suitable) definition for functional derivative in Curved space time
Thanks for your answer. May I ask you why you expect your points 9) , 10) to hold? That was the main point in my question.
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revised Is there a natural (suitable) definition for functional derivative in Curved space time
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asked Is there a natural (suitable) definition for functional derivative in Curved space time
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revised What is the variation of Gauss-Bonnet term a total derivative of?
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comment Conformal transformation/ Weyl scaling are they two different things? Confused!
Thanks I am clear about this point and I understand "undoing" by multiplying by the inverse of the function still gives a different space time. Where as conformal transformation does not change space-time just different coordinate label. I would try and attach a link to that paper then you might be able to tell where I am going wrong but not on this point. Thanks
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asked What is the variation of Gauss-Bonnet term a total derivative of?
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comment Conformal transformation/ Weyl scaling are they two different things? Confused!
Thanks a lot! it is clear when they are different. My confusion has to do with a paper I read. " Rev. Mod. Phys. 34, 442–457 (1962) Conformal Invariance in Physics" by L.Witten et al.. They talk about active point transformation and define a corresponding coordinate transformation to define a conformal transformation, which amounts to I think, rescaling the metric thus weyl transformation in our lingo. they call this $C_{g}$ however they say that special conformal transformation is a subgroup of these transformations with the usual lie-algebra in our lingo "conformal is a subgroup of weyl" ??