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Is renormalization associated with a volume scale or with an energy-momentum and length scale?

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Given that real-space renormalization blocks together small volume elements to construct larger volume elements, is it more appropriate/helpful to consider the renormalization scale to be a volume scale instead of an energy scale?

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asked Dec 25, 2011 in Theoretical Physics by Peter Morgan (1,230 points) [ no revision ]
retagged Mar 7, 2014 by dimension10

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Still a scale is just a quantity with dimension. If you have a volume scale, doesnt matter how you got it, you can take its root and get a length scale and vice versa.

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commented Dec 27, 2011 by Squark (1,725 points) [ no revision ]

Squark, I think you're right. One might be interested in other structure, but a scale is just a scale. Thanks.

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commented Dec 27, 2011 by Peter Morgan (1,230 points) [ no revision ]

OK, so question can be closed?

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commented Dec 28, 2011 by Squark (1,725 points) [ no revision ]

@Squark, you can vote to close, presumably as "not a real question". I tried to tease out a question here, but to my mind unsuccessfully. On the other hand, I don't want to make all decisions for the community.

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commented Jan 1, 2012 by Moshe (2,415 points) [ no revision ]

I'm not sure what harm having this question here does, nor am I sure what benefit there is in closing it. The point of the question is to ask whether anyone else is doing research in which this kind of distinction is of interest. I don't take it to be a strong argument unless you have yourselves done calculations in which such a distinction makes sense, but if one *is* interested in other structure than just scale, a volume scale is not the same as an energy scale.

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commented Jan 1, 2012 by Peter Morgan (1,230 points) [ no revision ]

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For a volume scale, one only needs the tensor $\epsilon^{\mu\nu\alpha\beta}$, one does not need any metric. This is splitting hairs at some level, of course, but I take it that conceptual progress is about making a personal choice of what distinctions to take seriously and which to put aside for another day.

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commented Dec 26, 2011 by Peter Morgan (1,230 points) [ no revision ]

You mean you want to consider a QFT which depends on a volume form but no metric? Do you have an example in 4D?

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commented Dec 26, 2011 by Squark (1,725 points) [ no revision ]

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