Timeline for Conserved quantities quantum field theory
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 16, 2020 at 10:50 | vote | accept | Faber Bosch | ||
| Nov 16, 2020 at 10:02 | answer | added | Richard Myers | timeline score: 3 | |
| Nov 7, 2020 at 17:31 | answer | added | Michele Grosso | timeline score: 1 | |
| Nov 7, 2020 at 17:14 | comment | added | Prof. Legolasov | @FaberBosch the operators $\phi(x)$ and $\pi(x)$ are already predetermined. You're probably confusing them with the expectation values and/or eigenvalues. | |
| Nov 7, 2020 at 16:48 | comment | added | Faber Bosch | @ChiralAnomaly "the field operators in QFT do obey EoMs" I don't understand this. How? The conjugate pairs $\hat{\phi}$ and $\hat{\pi}$ cannot be determined with precision simultaneously. Then how can there be an EoM? If there is an EoM you could know the history of field configurations for both conjugate operators. Can you elaborate your claim with an example, say, by writing down the EoM for a non-interacting quantum scalar field. | |
| Nov 7, 2020 at 16:37 | comment | added | Chiral Anomaly | @FaberBosch To clarify: when you say that the field operators in QFT don't have EoMs, do you mean that we can't write them in Euler-Lagrange form? Whether that's true or not, the field operators in QFT do obey EoMs (in the Heisenberg picture, which is the picture we always use in classical field theory), even though they don't commute. We use the EoMs to determine whether a given quantity is conserved. We don't need to use a lagrangian for this, so whether the lagrangian formalism works for non-commuting operators may or may not be relevant, depending on exactly what you're asking. | |
| Nov 7, 2020 at 5:59 | comment | added | Faber Bosch | @annav With this search keyword I mostly find QFT notes with mostly the same approach where Noerther's theorem is discussed in Classical Field Theory and never it is mentioned clearly when the quantum fields are discussed. | |
| Nov 7, 2020 at 5:30 | comment | added | Faber Bosch | @Qmechanic The question sounds similar but I want to know what happens in the canonical quantization formulation. I am not much familiar with path integrals and I have no idea what Ward-Takahashi identities are! | |
| Nov 7, 2020 at 4:39 | comment | added | Qmechanic♦ | Possible duplicate: Is there a formulation of Noether’s theorem for the path integral formalism? | |
| Nov 7, 2020 at 4:30 | history | asked | Faber Bosch | CC BY-SA 4.0 |