Register

Adv. Query

Q&A (4831)

Reviews (201)

Open problems (45)
Meta (437)

Site Statistics

205 submissions , 163 unreviewed
5,054 questions , 2,207 unanswered
5,345 answers , 22,720 comments
1,470 users with positive rep
818 active unimported users
More ...

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

1551 views

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?

This post has been migrated from (A51.SE)

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

Most voted comments show all comments

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.

This post has been migrated from (A51.SE)

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.

This post has been migrated from (A51.SE)

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

OK, so question can be closed?

This post has been migrated from (A51.SE)

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.

This post has been migrated from (A51.SE)

commented Jan 1, 2012 by Moshe (2,405 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.

This post has been migrated from (A51.SE)

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

Most recent comments show all comments

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.

This post has been migrated from (A51.SE)

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?

This post has been migrated from (A51.SE)

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

Your comment on this question:

To answer, leave an answer instead. Comments are usually for non-answers.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
To alert a user, please use the "@" command and remove spaces from the username, example, the user "John Doe" should be pinged as "@JohnDoe", while the user "Johndoe" should be pinged as "@Johndoe". The post author is always automatically pinged (unless you are the post author).
Please consult the FAQ for as to how to format your post.

Live preview (may slow down editor) Preview

Your name to display (optional):

Email me at this address if a comment is added after mine:

Privacy: Your email address will only be used for sending these notifications.

Anti-spam verification:

[captcha placeholder]

Please complete the anti-spam verification

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.

Live preview (may slow down editor) Preview

Your name to display (optional):

Email me at this address if my answer is selected or commented on:

Privacy: Your email address will only be used for sending these notifications.

Anti-spam verification:

If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysics$\varnothing$verflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).

Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights

...