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I'm going to answer this as a non- conformal field theorist, but I have been thinking about this stuff a bit lately. But I do believe I can answer the simplest of your questions: I'm sure an expert will put the following straight if there are mistakes. "So then a cordinate transformation which acts on the metric as a Weyl transformation is a conformal ...

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I am not sure if you mean $x$ one or two dimensional variable. I don't have the article at hand but I guess we probably mean $D=1$?? The argument goes as follows: you have to use Bochner's theorem, which says that $W(x-y):=W_2(x,y)$ is positive distribution if and only if the Fourier transformation yields is a positive measure $\tilde W(p) d^Dp$. In this ...

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The metric tensor $g_{\mu\nu}$ in 4 dimensions has 10 independent components. Each of these has the potential of being a dynamical degree of freedom, also know as a "mode." There are many different ways of parameterizing these 10 components. In general, of the 10 components, you can always pick one of them to correspond to the overall local scale of the ...

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Caveat: The first part of this answer takes a very technical stance on the BRST procedure, and additionally works with a finite-dimensional phase space for convenience. It could appear quite far from the understanding of ghosts in the average application of BRST transformations or ghosts as a tool. The general conception of ghosts There are many ...

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