Timeline for Spin-statistic for free quantum fields
Current License: CC BY-SA 4.0
16 events
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| Mar 30, 2021 at 13:40 | history | edited | Simon Henry | CC BY-SA 4.0 |
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| Mar 30, 2021 at 12:20 | answer | added | gmvh | timeline score: 2 | |
| Nov 19, 2020 at 11:18 | answer | added | Igor Khavkine | timeline score: 7 | |
| Nov 19, 2020 at 3:55 | comment | added | Aaron Bergman | But, I think more interesting to you might be Weinberg's version of spin-statistics where he shows (or argues at least -- it's not rigorous) that you can't have an interacting S-matrix that's consistent with causality unless you have the spin-statistics relation right. (And now I slink away embarrassed about how much QFT I've forgotten....) | |
| Nov 19, 2020 at 3:48 | comment | added | Aaron Bergman | So, it's been a while and I might get this embarrassingly wrong, but I think part of the answer is that you have a Hilbert space here, not a quantum field theory. To get a QFT, you're going to start playing with creation and annihilation operators and canonical commutation relations. Pretty soon things will go wrong if you have the wrong statistics (eg, your energy states will be unbounded below). | |
| Nov 18, 2020 at 22:20 | history | edited | Simon Henry | CC BY-SA 4.0 |
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| Nov 18, 2020 at 22:12 | comment | added | Simon Henry | I rewrote the question to try to adress the remarks made in the comment. @MichaelEngelhardt : I had read the wikipedia page and other text about this before, but for all these properties, either I do not understand what it is supposed to mean mathematically speaking, or it is satisfies by free quantum fields as describe above. | |
| Nov 18, 2020 at 22:09 | history | edited | Simon Henry | CC BY-SA 4.0 |
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| Nov 18, 2020 at 21:18 | comment | added | Michael Engelhardt | The wikipedia entry en.wikipedia.org/wiki/Spin-statistics_theorem for the spin-statistics theorem gives a pretty decent account of the necessary assumptions, which indeed are more specific than what you're assuming, also refuting some overly simplistic arguments along the way. | |
| Nov 18, 2020 at 20:49 | comment | added | Konstantinos Kanakoglou | I think it would be helpful for potential answerers to formulate tne questions in a more clear way. What i mean is that, the arguments presented in the OP are interesting, and the topic is clearly "hot" for any mathematical physicist, but the question(s) should be clearly formulated. If it is left on a level of "what does the spin statistics theorem says from a mathematical point of view ?" then it is too broad and one could write a review article or list a whole library of references. But i doubt that this is the point of the OP. | |
| Nov 18, 2020 at 20:33 | comment | added | Simon Henry | @AaronBergman : these Hilbert space comes with a representation of the (universal cover of) the Poincaré groups. Maybe there is more to it regarding Causality, but they inherit the "finite propagation speed" from the one particule space. | |
| Nov 18, 2020 at 20:32 | comment | added | Konstantinos Kanakoglou | What do you mean about the "bosonic fock space of a fermion"? On an algebraic basis the bosonic algebra (the first Weyl algebra) cannot have fin dim representations. So there is no fermionic space for it. On the other hand, the fermionic algebra is a nilpotent one. It fock rep is a fin dim one. So there is no "bosonic space" for it. These can be easily distinguished on an algebraic setting. | |
| Nov 18, 2020 at 20:31 | comment | added | Simon Henry | @KonstantinosKanakoglou : I mean the Bosonic Fock space of a half integer spin representation. | |
| Nov 18, 2020 at 20:28 | comment | added | Aaron Bergman | You need to impose Poincare invariance and causality. | |
| Nov 18, 2020 at 19:46 | history | edited | YCor | CC BY-SA 4.0 |
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| Nov 18, 2020 at 19:40 | history | asked | Simon Henry | CC BY-SA 4.0 |