162:"Physically speaking, topological field theories are not especially interesting. They are toy models, far simpler in structure than the quantum field theories which describe real-world physics. They can be thought of as warm-up exercises for the much harder task of quantizing gravity. Quantum gravity is believed to be background-independent (in some suitable sense), and TQFTs provide examples of background independent quantum field theories. Unfortunately, they are only background independent in a fairly trivial sense: they are independent of the spacetime metric (thought of as a background gravitational field), but they do not admit any local degrees of freedom. There is no radiation in a TQFT: no propagating waves, no gluons, no gravitons."
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I am curious for some references on this section on fixed spacetime, i just saw a fantastic talk on the topic and am interested in reading more, i am interested in where this info is from, also in general having more references would be greatm perhaps a recommended reading? Sean, a student 21:42, 7
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Dear PKT. Thanks for your pointing out this point! I intend to refer partition function in quantum field theory. But there are several partition functions, which essentially should be as same as each other, I think. I will fixed it according to your advice. I wonder which partition function is
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I have fixed the kind of correlation functions and partition functions to "correlation function (quantum field theory)" and "partition function (quantum field theory)" but I am more interesting in the article of them (statistical mechanics) or (mathematics) than the ones (quantum field
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It is promoting
Ovchinnikov's work, which can be found on arxiv if references are needed, but the idea presented in the article, that casting everything as a TQFT is either possible or productive has not caught on.
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Even though I have already seen this classification in physics, I don't understand where typical topological sigma-models fit into it, p.ex. Poisson sigma model (), Courant sigma model () or Dirac sigma model ().
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Dear someone who described firstly the part of the article about relations between TQFT and (co)bordism; Would you mind completing the article where has expressed as "" or introducing me some references.
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I'm going to describe the Atiyah's original axioms from his papers in 1980's. I will write the original axioms, relations to physics and some examples and add some reference of them.
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Large parts of this article are taken verbatim from Atiyah's article. (Sometimes, a few sentences are left out so that it becomes non-sensical.) --
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Dear John Baez: Thanks for your deleting the irrelevant reference. I did not translate it into
Japanese by the same reason last year.--
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According to papers of Sir Atiyah, I have summarized the outline of the quantum field theory, in particular of the initial phase.--
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Quite impressing introduction. Even though I think the emphasize on a metric background is a bit strong (p.ex.
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Implying that TQFTs don't "describe real-world physics" is inconsistent with the preceding paragraph.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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I think the "Topological Dipole Theory" reference is completely random and needs to be removed.
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Can you give references of good introductions/ overviews. A review article would be nice.
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I improve some sentences in "Witten-Type TQFT" and change some links. --
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Reference missing the "Witten-type TQFTs and dynamical systems" section
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I'm assuming that there's a confusion here, and editing accordingly.
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There are no reference to any of the claims in that section.
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Thanks someone for your correction of my spell miss. --
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