Timeline for Hamilton formalism for Dirac spinors
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| Oct 2, 2023 at 18:16 | comment | added | Xenomorph | That's the Poisson bracket for bosons. The Poisson bracket of fermions is different. | |
| Mar 21, 2014 at 15:12 | history | edited | Hunter | CC BY-SA 3.0 |
added 18 characters in body
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| Mar 21, 2014 at 4:35 | vote | accept | Andrew McAddams | ||
| Mar 20, 2014 at 13:05 | comment | added | Andrew McAddams | @Hunter : unfortunately, I was wrong: spinors component aren't grassmanian numbers (even in classical limit) as long as we don't use anticommutation relations. | |
| Mar 19, 2014 at 22:13 | comment | added | Hunter | @AndrewMcAddams Sure, I would be very interested. Where are you posting it? | |
| Mar 19, 2014 at 22:03 | comment | added | Andrew McAddams | @Hunter : it seems that I showed it. May you check, if you please? | |
| Mar 19, 2014 at 21:07 | comment | added | Hunter | @AlexNelson no I didn't take your comments negatively at all. I really like to learn, and thus I only appreciate your comment. It always good to be aware of possible caveats. | |
| Mar 19, 2014 at 21:05 | comment | added | Alex Nelson | @Hunter, another good preprint: "On the Hamilton-Jacobi formalism for fermionic systems" arXiv:math-ph/0311016. I hope you don't take my comments negatively, I was actually hoping you could refresh my memory: you explain things very well! | |
| Mar 19, 2014 at 21:02 | comment | added | Andrew McAddams | @Hunter : I intuitively think that the correspondence principle in a case of spinors already contains postulates which gives us anticommutation relations, but I still don't prove that. So I'll check it in the near future. [:)]. | |
| Mar 19, 2014 at 20:57 | comment | added | Hunter | @AndrewMcAddams thanks, I won't delete it then :). If I understand you correctly, you would like to "derive" the anti-commutation relations from the Poisson bracket? I don't think this is possible. I believe that the anti-commutation relations (just like the commutation relations) in QFT are simply postulates. | |
| Mar 19, 2014 at 20:55 | comment | added | Hunter | @AlexNelson so much to learn, not enough time. Thanks for the link though, will definitely have a look at that. | |
| Mar 19, 2014 at 20:54 | comment | added | Andrew McAddams | @Hunter : no, your question is very useful for me. It leaves only one "dark side": the "possibility" of getting the anticommutation relations for fields directly from the Poisson brackets for spinors. I hope I will get it. | |
| Mar 19, 2014 at 20:53 | comment | added | Alex Nelson | @Hunter, don't get me wrong, your answer is a great overview for most fields. I wish I had your answer handy when I began learning field theory :) But classical spinors are wacky on a good day...I'll try to dig up my notes on this when time allows (it may take weeks), as I myself would be interested in re-learning this. In the meantime, I found this preprint: "Poisson Bracket for Fermion Fields" arXiv:1211.4231 | |
| Mar 19, 2014 at 20:49 | comment | added | Hunter | @AndrewMcAddams I'm not sure what your question is. I had to Google what Dirac brackets are and I have not yet studied this in detail (see the post above). I was under the impression you wanted to know the quantization procedure from Poisson brackets to (anti-)commutation rules. If this is not true (maybe I misinterpreted your question and I won't be able to answer your actual question), then I'm happy to delete my answer. | |
| Mar 19, 2014 at 20:45 | comment | added | Hunter | @AlexNelson I have no idea, because I have not (yet) studied constraints in quantum field theory (except for Gauss' constraint). I would be interested to read about it if you feel like writing an answer :). | |
| Mar 19, 2014 at 20:40 | comment | added | Andrew McAddams | Thank you! But can we get the "+" (anticommutator's) sign in the correspondense of Poisson and the Dirac bracket. May it be done as the result of the grassmanian nature of the spinors? | |
| Mar 19, 2014 at 20:40 | comment | added | Alex Nelson | Don't spinors have the peculiarity that we need to consider the Dirac Bracket? The Lagrangian is linear in velocity, after all...I seem to vaguely recall reading this in Henneaux and Teitelboim's Quantization of Gauge Systems... | |
| Mar 19, 2014 at 20:37 | history | edited | Qmechanic♦ | CC BY-SA 3.0 |
In this context is seems illuminating to write hbar explicitly. Dear Hunter, if u don't like my changes please roll back or use the parts u like.
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| Mar 19, 2014 at 20:30 | history | edited | Hunter | CC BY-SA 3.0 |
deleted 6 characters in body
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| Mar 19, 2014 at 20:25 | history | answered | Hunter | CC BY-SA 3.0 |