Timeline for Dimensionless vs. dimensional RG-Flow equations
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Oct 7, 2021 at 0:58 | answer | added | N0va | timeline score: 2 | |
| Aug 30, 2021 at 17:49 | comment | added | Antihero | At Andrew: I editet the post. At bbrink: I think that your statement, that non-rescaled flow equations do not have fixed points is wrong, can you tell me my error? - Writing $\mathrm{d}_{ \Lambda } \vec{ \gamma } = \vec{ \gamma }^{ \operatorname{T}} \cdot B \cdot \vec{ \gamma}$ gives solutions with $\mathrm{d}_{ \Lambda} \vec{\gamma} = 0$ if $\vec{ \gamma}$ is in the kernel of the matrix B. There is no need to rescale the flow equations, in order to find fixed points. (???) | |
| Aug 30, 2021 at 17:49 | history | edited | Antihero | CC BY-SA 4.0 |
Added the "EDIT"-Part.
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| Aug 1, 2021 at 16:03 | comment | added | Ratman | I am not sure OP question aim at this, but more avout relations between dimensional analysys and renormalization group can be found in Goldenfeld book and in Barenblatt book on scaling and intermediate asymptotics | |
| Aug 1, 2021 at 15:40 | comment | added | bbrink | Echoing Andrew, I'm not familiar with the reference, but my guess is that the issue is related to the rescaling step of the RG, which often involves non-dimensionalizing the flow equations using the running scale (e.g., momentum in a momentum-shell calculation). If so, then the answer is that the dimensionful/non-rescaled flow equations do not have fixed points, similar to how the diffusion equation $c_t = c_{xx}$ does not have a stationary solution $c(t,x) = c(x)$, but setting $c(t,x) = f(x/\sqrt{t})/\sqrt{t}$ does yield a stationary solution for $f(y)$ with $y = x/\sqrt{t}$. | |
| Aug 1, 2021 at 3:06 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
added 6 characters in body; edited tags
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| Aug 1, 2021 at 3:05 | comment | added | Andrew | Would you be able to give an example of "dimensional" and "dimensionless rescaled" RG equations? (I don't have your book handy) Based on your description it sounds like you are essentially asking about the difference between (a) how a dimensionful coupling scales with energy (which will include contributions from both the "boring" engineering dimension you would guess from dimensional analysis and the "interesting" quantum corrections), and (b) the anomalous dimension of an operator, which is just the "interesting" part. But, I'm not 100% sure, without more detail. (Maybe someone else knows). | |
| Aug 1, 2021 at 2:18 | history | asked | Antihero | CC BY-SA 4.0 |