Timeline for Dirac spinor's non-unitary representation of the Poincaré group leads me to conclude that Dirac spinors are not "quantum states" in the usual sense
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 21, 2021 at 2:14 | vote | accept | Nicholas Engelbert | ||
| Jun 21, 2021 at 2:10 | answer | added | Chiral Anomaly | timeline score: 7 | |
| Jun 21, 2021 at 0:09 | comment | added | DanielC | („Classical”) Dirac fields (in the Lagrangian or Hamiltonian formulation) become observables through quantization, not states. | |
| Jun 20, 2021 at 23:12 | comment | added | Charlie | Note also that in non-relativistic quantum mechanics the $\mathfrak su(2)$ representation used to attach spin to particles does not admit a unitary representation of the Poincaré algebra but the states $|\uparrow\rangle$ and $|\downarrow\rangle$ etc. are still considered "quantum states". | |
| Jun 20, 2021 at 23:11 | comment | added | Charlie | This is the point of quantisation, the finite-dimensional Poincaré algebra reps are necessarily not unitary. However, after we "quantize" the field, $\psi(x)$ becomes an operator and it is on this infinite-dimensional Hilbert space that the Poincaré algebra can be represented unitarily. | |
| Jun 20, 2021 at 23:00 | history | asked | Nicholas Engelbert | CC BY-SA 4.0 |