Timeline for Problem of quantization: state of the art
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 25, 2012 at 16:16 | vote | accept | Sadiq Ahmed | ||
| Sep 21, 2012 at 10:55 | answer | added | Sadiq Ahmed | timeline score: 0 | |
| Sep 20, 2012 at 19:49 | comment | added | Alexander Chervov | mathoverflow.net/questions/19495/… | |
| Sep 20, 2012 at 17:12 | answer | added | Palle Jorgensen | timeline score: 2 | |
| Sep 19, 2012 at 16:12 | comment | added | Alexander Chervov | No go theorem is called van Hove theorem - I remember it in Hurt's Geometric quantization, i do not have this book now. google gives some references - I am not sure what is the best.... | |
| Sep 19, 2012 at 13:56 | comment | added | Igor Khavkine | This is essentially the same question as the one Joel linked to, made slightly more narrow. Why not just edit the original question and ask for it to be reopened? | |
| Sep 19, 2012 at 13:27 | comment | added | JRN | See also mathoverflow.net/questions/107323/… | |
| Sep 19, 2012 at 12:29 | comment | added | Alexander Chervov | Under this relaxed condition the case of R^2n is more or less covered by standard correspondence p-> d/dx q->x. Moreover this problem can be generalized to symplectic manifolds - see section 5. Berezin and Berezin-Toeplitz quantization on K¨ahler manifolds in the reference. Actually one hopes something similar for Poisson manifolds - to each symplectic leave should correspond an operator representation. But this is subtle project even in the case of Lie algebras - where this reduces to the "orbit method" there are many problems. | |
| Sep 19, 2012 at 12:22 | comment | added | Alexander Chervov | Requirement 1.4 is not enlighting \hat {f,g} = [\hat f ,\hat g ] , this should not hold on any large class of observables... The correct definition is notion of deformation quantization - [\hat f ,\hat g ] = h \hat {f,g} + O(h^2) , where by \hat f I mean correspondence from classical to quantum. | |
| Sep 19, 2012 at 12:00 | history | edited | Sadiq Ahmed | CC BY-SA 3.0 |
deleted 4 characters in body; edited title
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| Sep 19, 2012 at 11:48 | history | asked | Sadiq Ahmed | CC BY-SA 3.0 |