Timeline for What is the relationship between spinors and supermanifolds and fermions?
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| Sep 14, 2020 at 19:36 | comment | added | Aaron Bergman | @TimCampion Yes and no. You can say that fermions are fundamentally quantum mechanical and stop there, but physicists like to do path integrals, which are based on 'classical' actions and involve multiplying (and integrating!) these classical fields. Thus, the formalism of anti-commuting fields/Grassman variables and Berezin integration was used (developed?). Basically, you develop the formalism so that the path integral gives the right answer for fermions, and you can think of the anti commuting fields/Grassman variables as being the (semi-)classical limit of the quantum fields. | |
| Sep 14, 2020 at 19:04 | comment | added | Tim Campion | Thanks! So it seems the conclusion I took from the other answer was wrong -- (1) and (2) are not equivalent at all! There are many things I still don't understand, but I think the most pressing one is the phrase "anticommutative field" -- because I don't understand this operation of "multiplying" field configurations. Am I correct in understanding that the phrase "anticommutative field" is meaningless classically, and only has meaning when you are doing quantum physics, where observables are supposed to form an algebra? | |
| Sep 14, 2020 at 18:52 | history | edited | LSpice | CC BY-SA 4.0 |
Name of Dan Freed's notes
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| Sep 14, 2020 at 15:49 | history | edited | Aaron Bergman | CC BY-SA 4.0 |
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| Sep 14, 2020 at 15:20 | history | answered | Aaron Bergman | CC BY-SA 4.0 |