Timeline for Why can we use the equation of motion to calculate the amplitude in "Quantum Field Theory"?
Current License: CC BY-SA 4.0
7 events
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| Aug 10, 2019 at 15:15 | comment | added | octonion | @TangBear, You are correct, the classical equations of motion (sometimes modified by anomalies) hold for operators in QFT just like in the Ehrenfest theorem, and this carries over to properties of amplitudes. | |
| Aug 10, 2019 at 10:25 | vote | accept | Kimari | ||
| Aug 10, 2019 at 10:24 | comment | added | Kimari | I brought up the Ehrenfest theorem as an example of why the equation of motion can be written in quantum system. I got confused because when I look at the Feynman prescription, equation of motion does not have any meaning (since we can get the equation of motion only when the action is extremised). When I make an analogy to Ehrenfest, things become more transparent. In classical system, you can have equation of motion $\frac{dx}{dt}=\frac{p}{m}$, which is meaningless in quantum mechanics. It can be correct in quantum only if you promote them to the operator level (obtained using Ehrenfest) | |
| Aug 10, 2019 at 9:17 | comment | added | Oбжорoв | @TangBear I am really not sure why you need to bring in Ehrenfest's theorem. I have added a paragraph to hopefully clarifies it completely. If you agree with this answer can you accept it? Tx. | |
| Aug 10, 2019 at 9:14 | history | edited | Oбжорoв | CC BY-SA 4.0 |
added second paragraph to make it clearer following a comment from the OP
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| Aug 9, 2019 at 13:19 | comment | added | Kimari | I think I understood what you meant now. If we make an analogy to the harmonic oscillator, we can see that the Ehrenfest's theorem will give the equation of motion of the "operator" in the Heisenberg picture, but that does not imply a "classical equation of motion" at all. In this case, it should be the same as well, if we regard every field to be operator. The equation of motion is "vaguely" similar to those obtained from the Ehrenfest. Do I understand this correctly? | |
| Aug 9, 2019 at 11:54 | history | answered | Oбжорoв | CC BY-SA 4.0 |