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This article may be too technical for most readers to understand.(September 2010) |
This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 09:46, 10 November 2007 (UTC)
How on earth is conformal field theory of low importance? It's one of the active research areas of quantum field theory, because it's needed to state the AdS/CFT correspondence, which, in the words of the article, is "the most highly cited article in the field of high energy physics."
Warning: Once this gets a higher importance, I'll start griping about it's class rating! Adam1729 ( talk) 02:32, 8 October 2015 (UTC)
Actually this article is High importance in my opinion - adjusted, and is in dire need of rewriting since it's a total mess. PhysicsAboveAll ( talk) 12:55, 9 October 2015 (UTC)
There was a reference to "Critical point (mathematics)" at the end of the article. Seems a bit too elementary, maybe the editor meant "Critical point (physics)" which is much more relevant? Applying changes, please revert if you think necessary. —Preceding unsigned comment added by 150.203.179.241 ( talk) 00:36, 30 June 2010 (UTC)
The examples of the Ising, Potts, and random cluster models at criticality used in most articles (i've read) are classical -i might be mistaken but it seems Ising and Lenz thought in classical terms when defining the Ising model. That is, we have a measure on classical arrangements of the classical spins (without arguing whether spin is intrinsically quantum mechanical) and not a measure on a magnitization field, or on a lattice-indexed family of quantum spin states (qubits, elements of a 2D Hilbert space). And those theories are considered conformal field theories, the field being then a random classical field. Shouldn't the notion of conformal field theory be wider than just requiring it to be quantum ? Of course most of the formalism (computations of correlations functions, OPEs) apply regardless of the "microscopic" definition of the theory, and many results are exactly the same when we can consider a classical and quantum version of a system, like for Ising models, but a classical statistical model is just not quantum. So i think we should just focus on conformal invariance and not require quantumness in general.
Also, i am not an expert but it seems to me that conformal invariance also requires the notion of boundaries, to be defined rigorously, otherwise the conformal transformations are not well-defined, at least in 2D, unless we restrict just to global conformal (Möbius) transformations. In probability they define conformal invariance in terms of the image of domains of the complex plane and curves inside those regions; they have a measure on such curves (for instance the 2D Wiener measure), which is invariant by composition with conformal transformations -the term "covariant" can also be used instead, as the measure is strictly-speaking not invariant, unless the conformal transformation is the identity. See for instance Gregory Lawler's https://inis.iaea.org/collection/NCLCollectionStore/_Public/38/098/38098204.pdf
So i would say that because conformal field theory is getting alot of attention from mathematicians it would be interesting to cater to publics that likes more precision and generality, in this article, by defining/stating things a little more rigorously. Plm203 ( talk) 07:04, 14 June 2023 (UTC)
The discussion on classical vs quantum above is confusing. It seems the author of the question means rather Euclidean vs Lorentzian. It's true that Euclidean CFTs are used for describing critical phenomena in classical stat-mech models, while Lorentzian CFTs arise in describing (quantum) phase transitions in quantum cond-mat models. But both Euclidean CFTs and Lorentzian CFTs are quantum, in the sense that there is behind a Hilbert space with operators acting on it.
PhysicsAboveAll (
talk) 19:01, 16 June 2023 (UTC)
This
level-5 vital article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||
|
This article may be too technical for most readers to understand.(September 2010) |
This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 09:46, 10 November 2007 (UTC)
How on earth is conformal field theory of low importance? It's one of the active research areas of quantum field theory, because it's needed to state the AdS/CFT correspondence, which, in the words of the article, is "the most highly cited article in the field of high energy physics."
Warning: Once this gets a higher importance, I'll start griping about it's class rating! Adam1729 ( talk) 02:32, 8 October 2015 (UTC)
Actually this article is High importance in my opinion - adjusted, and is in dire need of rewriting since it's a total mess. PhysicsAboveAll ( talk) 12:55, 9 October 2015 (UTC)
There was a reference to "Critical point (mathematics)" at the end of the article. Seems a bit too elementary, maybe the editor meant "Critical point (physics)" which is much more relevant? Applying changes, please revert if you think necessary. —Preceding unsigned comment added by 150.203.179.241 ( talk) 00:36, 30 June 2010 (UTC)
The examples of the Ising, Potts, and random cluster models at criticality used in most articles (i've read) are classical -i might be mistaken but it seems Ising and Lenz thought in classical terms when defining the Ising model. That is, we have a measure on classical arrangements of the classical spins (without arguing whether spin is intrinsically quantum mechanical) and not a measure on a magnitization field, or on a lattice-indexed family of quantum spin states (qubits, elements of a 2D Hilbert space). And those theories are considered conformal field theories, the field being then a random classical field. Shouldn't the notion of conformal field theory be wider than just requiring it to be quantum ? Of course most of the formalism (computations of correlations functions, OPEs) apply regardless of the "microscopic" definition of the theory, and many results are exactly the same when we can consider a classical and quantum version of a system, like for Ising models, but a classical statistical model is just not quantum. So i think we should just focus on conformal invariance and not require quantumness in general.
Also, i am not an expert but it seems to me that conformal invariance also requires the notion of boundaries, to be defined rigorously, otherwise the conformal transformations are not well-defined, at least in 2D, unless we restrict just to global conformal (Möbius) transformations. In probability they define conformal invariance in terms of the image of domains of the complex plane and curves inside those regions; they have a measure on such curves (for instance the 2D Wiener measure), which is invariant by composition with conformal transformations -the term "covariant" can also be used instead, as the measure is strictly-speaking not invariant, unless the conformal transformation is the identity. See for instance Gregory Lawler's https://inis.iaea.org/collection/NCLCollectionStore/_Public/38/098/38098204.pdf
So i would say that because conformal field theory is getting alot of attention from mathematicians it would be interesting to cater to publics that likes more precision and generality, in this article, by defining/stating things a little more rigorously. Plm203 ( talk) 07:04, 14 June 2023 (UTC)
The discussion on classical vs quantum above is confusing. It seems the author of the question means rather Euclidean vs Lorentzian. It's true that Euclidean CFTs are used for describing critical phenomena in classical stat-mech models, while Lorentzian CFTs arise in describing (quantum) phase transitions in quantum cond-mat models. But both Euclidean CFTs and Lorentzian CFTs are quantum, in the sense that there is behind a Hilbert space with operators acting on it.
PhysicsAboveAll (
talk) 19:01, 16 June 2023 (UTC)