Timeline for What is the algebraic property that corresponds to a topological term?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Aug 28, 2022 at 15:29 | history | edited | Urb | CC BY-SA 4.0 |
deleted 8 characters in body
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| S Aug 27, 2022 at 21:17 | history | suggested | Glorfindel | CC BY-SA 4.0 |
broken link fixed, cf. https://meta.mathoverflow.net/q/5301/70594
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| Aug 27, 2022 at 18:08 | review | Suggested edits | |||
| S Aug 27, 2022 at 21:17 | |||||
| Aug 22, 2013 at 8:35 | comment | added | Trimok | @DavidBarMoshe : +1, especially for the reference to the seminal article by Orlando Alvarez, which is very readable. | |
| Aug 21, 2013 at 17:16 | comment | added | BebopButUnsteady | Also I realize that WZW terms are kind of a bad choice of topological term since, as you say, they correspond to the fact there is no naive Hilbert space. Since I come from a condensed matter background I am used to thinking of WZW theories as edges of actual objects, and these objects still have a normal Hilbert space. | |
| Aug 21, 2013 at 17:04 | comment | added | BebopButUnsteady | "I assume you mean the quantum theory is defined by a path integral". Actually, quite the reverse. I want to think of the Hilbert space/Hamiltonian("algebraic side") as fundamental, since I have learned the hard way about the ambiguities. But topological terms are so pretty in the path integral form and I don't understand what they correspond to on the "algebraic side". I think I am asking about seeing it from "the quantum linear structure you are trying to dequantize", but I'm not sure that your "quantum linear structure" is my "algebraic side". | |
| Aug 21, 2013 at 16:42 | comment | added | David Bar Moshe | 2) When you say that you want to go from quantum to classical, I assume that you mean that the quantum theory is defined by means of a path integral, but in general path integrals are ambiguous, and also it is hard to see from them the quantum linear structure that you want to dequantize, this is why I think that methods of geometric quantization are superior. | |
| Aug 21, 2013 at 16:41 | comment | added | David Bar Moshe | @BebopButUnsteady Yes, that what I am trying to tell. The quantization point of view is quite unifying of various physical ideas. But, let me first remark: 1) The WZW terms already change the symplectic structure in the classical theory, not only that but they can spoil the closure of the Jacobi identities resulting nonassociativity and lack of Hilbert space representation of the quantum theory. | |
| Aug 21, 2013 at 16:23 | comment | added | BebopButUnsteady | So what I think you're telling me is that my question is basically equivalent to the problem of quantization (or at least pre-quantization), since the 1) target space of the sigma model is the classical phase space and 2) the topological terms differentiate between different quantum theories with the same classical phase space 3) The problem of associating all quantum theories with a given classical space is the hard problem of quantization. But I have some feeling I am asking for less, since I want to go quantum to classical, and I don't think I'm asking for a complete classification. | |
| Aug 21, 2013 at 11:34 | history | answered | David Bar Moshe | CC BY-SA 3.0 |