A_B
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Hi,
I'm confused about the discussion on p28 of Nigel Goldenfeld's "Lectures on phase transitions and the renormalization group" (this question can only be answered by people who have access to the book.)
The goal is to compute the potential energy of a uniformly charged sphere where the interaction potential goes as [itex]1/r^\sigma[/itex] (So Gauss's law isn't valid). I think that, after the change of variables (x,y) -> (u, v) he neglects to restrict the range of u to the intersection of two unit spheres that are translated a distance v with respect to each other. The final result of the computation also does not agree with the case [itex]\sigma=2[/itex].
This is however not mentioned the errata (http://guava.physics.uiuc.edu/~nigel/errata.html) so maybe I'm missing something.Thanks,
A_B
I'm confused about the discussion on p28 of Nigel Goldenfeld's "Lectures on phase transitions and the renormalization group" (this question can only be answered by people who have access to the book.)
The goal is to compute the potential energy of a uniformly charged sphere where the interaction potential goes as [itex]1/r^\sigma[/itex] (So Gauss's law isn't valid). I think that, after the change of variables (x,y) -> (u, v) he neglects to restrict the range of u to the intersection of two unit spheres that are translated a distance v with respect to each other. The final result of the computation also does not agree with the case [itex]\sigma=2[/itex].
This is however not mentioned the errata (http://guava.physics.uiuc.edu/~nigel/errata.html) so maybe I'm missing something.Thanks,
A_B