Timeline for Why is a critical quantum system described by a conformal theory in one higher dimension of space?
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15 events
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| May 11, 2012 at 8:42 | history | edited | Ron Maimon | CC BY-SA 3.0 |
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| May 10, 2012 at 17:10 | comment | added | Olaf | You should think of the mapping as "temperature + spatial coordinate" <--(maps to)--> "compactified imaginary time + spatial coordinate". So the 1D quantum system at finite temperature at equilibrium is described by a 2D field theory, where one of the coordinates of the field theory is periodic and describes the temperature of the original system. Then the fact that the 1D system is critical is the reason why this 2D field theory is conformal. | |
| May 10, 2012 at 16:12 | answer | added | Arnold Neumaier | timeline score: 2 | |
| Dec 22, 2011 at 12:23 | comment | added | Calvin | @genneth I'd be really grateful if you could clarify this for me. | |
| Dec 16, 2011 at 20:19 | comment | added | Calvin | @genneth Thanks, but how can a 1-dimensional quantum system be a 2-dimensional conformal field theory? - What does that have to do with the dimensions being spatial? | |
| Dec 16, 2011 at 16:47 | comment | added | genneth | All of this is about equilibrium --- so the time dimension doesn't matter. The dimensionality mentioned here are all spatial. | |
| Dec 15, 2011 at 16:07 | comment | added | Calvin | @genneth But a conformal field theory is quantum, not classical, isn't it? - How can a 1-dimensional quantum system be a 2-dimensional conformal field theory? (Should that be 1+1-dimensional conformal field theory?) For example, arXiv:hep-th/0603001 writes this. | |
| Dec 13, 2011 at 23:57 | comment | added | genneth | I'm not sure I understood what you said; but assuming I did: yes --- a quantum field theory in $d$-dimensions has the same partition function as a classical field theory in $d+1$-dimensions. | |
| Dec 13, 2011 at 21:12 | comment | added | Calvin | @genneth So a finite temperature d-dimensional many-body system is not necessarily a field theory, and this is why a (d+1)-dimensional classical field theory describes it in path integral form? | |
| Dec 12, 2011 at 17:00 | comment | added | genneth | a CFT is just a field theory with some special symmetries. As Ron alludes to in his answer, the equilibrium properties of a quantum field theory in $d$ dimensions at finite temperature is given by a $d+1$-dimensional classical field theory (if this is not clear, please say so). | |
| Dec 12, 2011 at 13:05 | comment | added | Calvin | @genneth I am familiar with path integrals - I thought that was the answer to the 2nd and third questions, but nowhere seems to say it explicitly. But it's the first question I'm really stuck on, and I don't know enough about CFT to know if it's somehow related to path integrals too. | |
| Dec 12, 2011 at 11:51 | comment | added | genneth | Are you familiar with path integral approach to thermal/statistical field theory? If not, that would be why this is puzzling to you --- and an answer can focus on that. | |
| Dec 12, 2011 at 11:07 | answer | added | Ron Maimon | timeline score: 1 | |
| Dec 11, 2011 at 17:01 | history | edited | Calvin |
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| Dec 11, 2011 at 16:10 | history | asked | Calvin | CC BY-SA 3.0 |