Timeline for Do I run into trouble if I interpret the fermionic field operator as a linear combination of a real and an imaginary part?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Oct 19, 2021 at 22:00 | comment | added | Chiral Anomaly | Let us continue this discussion in chat. | |
| Oct 19, 2021 at 19:20 | comment | added | Quantumwhisp | @ChiralAnomaly I'm aware that this eigenstates I'm talking about then would need to have grassman numbers as eigenvalues | |
| Oct 19, 2021 at 18:54 | comment | added | Quantumwhisp | @ChiralAnomaly Just to get you right on this: The problem you describe is resolved by letting any VEV involving only a single field operator to be zero, and that is what you mean by "observable" (Is that right?). When I write "observable" however, I only mean that the operator is hermitean, because then the eigenstates of the operator form a complete set. Or do you mean that this is prevented as well? | |
| Oct 19, 2021 at 14:09 | comment | added | Quantumwhisp | @ChiralAnomaly I get the problem, And you say that I would run into the same problem with the operator $\psi_{real}$ that I proposed? | |
| Oct 19, 2021 at 13:41 | comment | added | Chiral Anomaly | @Quantumwhisp Microcausality says that observables must commute with each other at spacelike separation. Otherwise, faster-than-light communication would be possible. Spin-statistics says that spinor fields cannot commute with each other at spacelike separation (in other words, spinor fields must be fermion fields), because otherwise the total energy would not have a lower bound. So if you don't want faster-than-light communication and do want a stable vacuum state, then spinor fields can't be observables. Is this the kind of trouble you're asking about? | |
| Oct 19, 2021 at 13:23 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
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| Oct 19, 2021 at 13:12 | comment | added | Quantumwhisp | @ChiralAnomaly do you mean the anticommutation relations which ensure microcausality? How would they make any trouble? | |
| Oct 19, 2021 at 13:11 | comment | added | Quantumwhisp | @knzhou I'm not looking for a classical limit, I'm looking for a meaning-ful way what an operator that undergoes time evolution represents. I have a good chunk of understanding when it comes to observables, but for every other operator, I'm hanging in the air, and that's why I proposed my little trick. | |
| Oct 19, 2021 at 8:41 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
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| Oct 19, 2021 at 1:18 | answer | added | Qmechanic♦ | timeline score: 3 | |
| Oct 19, 2021 at 1:00 | comment | added | Chiral Anomaly | The problems that you'll run into depend on what you already know. Are you familiar with the reason for the spin-statistics connection and/or the reason for the microcausality principle? | |
| Oct 19, 2021 at 0:54 | comment | added | Wouter | These two fields are Majorana's , no? | |
| Oct 19, 2021 at 0:41 | answer | added | ShoutOutAndCalculate | timeline score: 0 | |
| Oct 19, 2021 at 0:19 | comment | added | knzhou | That is "allowed", but it won't make you feel any happier. The underlying reason you're uncomfortable is because you're familiar with classical fields like the electromagnetic field, and you want an analogous classical field limit for fermionic fields. But such a description can't exist since the classical field limit requires large occupancy numbers, which are impossible for fermions. The fact that some fermion fields are complex is irrelevant, their fermionic nature is the real issue. | |
| Oct 19, 2021 at 0:15 | history | asked | Quantumwhisp | CC BY-SA 4.0 |