Timeline for Nature of Spin in QFT
Current License: CC BY-SA 4.0
12 events
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| Feb 13, 2019 at 18:22 | comment | added | CSnowden | I'll try to rephrase my question. Is the symmetry expressed by the group SL(2,C) a property of the specific wave function of the electron matter field (in Hilbert space) - in that sense the answer to my original, broad question would be that intrinsic spin is more a property of the excitation of the electron matter field, but more highly structured than my original basic statement about being asymmetric. | |
| Feb 13, 2019 at 9:13 | comment | added | InertialObserver | @CSnowden If you are leaning QFT, learning this terminology is necessary for a complete understanding.. I take it you are at least almost graduated or are in grad school.. If not, then considering QFT to understand spin is probably not the best idea | |
| Feb 13, 2019 at 3:44 | comment | added | CSnowden | Can you please translate from the formal mathematics (which I am not able to follow) to the conceptual basis? | |
| Feb 12, 2019 at 22:35 | history | edited | InertialObserver | CC BY-SA 4.0 |
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| Feb 12, 2019 at 22:35 | comment | added | InertialObserver | I think I see.. So the Poincare group is made up of these finite dimensional irreps, but it itself is infinite dimensional (unitary) representation, is what I'm gathering | |
| Feb 12, 2019 at 22:27 | comment | added | ACuriousMind♦ | It is irreducible. It is just not unitary, and it doesn't have to be - only the quantum space of states needs a unitary rep. | |
| Feb 12, 2019 at 22:23 | comment | added | InertialObserver | I see.. but then how can we say that the (1/2,0) spinor is an irrep of the PG if it’s only dimension 2, or is that wrong too? | |
| Feb 12, 2019 at 22:18 | comment | added | ACuriousMind♦ | The latter. A chiral spinor field lives in two dimensions, its particle states live in an infinite-dimensional Hilbert space. It is the latter space upon which a unitary representation exists. | |
| Feb 12, 2019 at 22:17 | comment | added | InertialObserver | In what sense exactly are those reps infinite dimensional? My understanding was that a chiral spinor lives in a two dimensional complex space. Or are you saying that is the case, but that’s not a unitary representation of the PG? | |
| Feb 12, 2019 at 19:29 | comment | added | ACuriousMind♦ | There's a bit of terminological confusion in this answer: The unitary representations of the Poincaré group are all infinite-dimensional and not the finite-dimensional representations denoted by a pair of half-integers $(s_1,s_2)$ you talk about later. | |
| Feb 12, 2019 at 0:45 | history | edited | InertialObserver | CC BY-SA 4.0 |
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| Feb 11, 2019 at 22:40 | history | answered | InertialObserver | CC BY-SA 4.0 |