Can you do some videos based on PATH INTEGRAL for qft (i.e. for photon field, fermionic field, scalar field) because I really need help about this over the course of my graduating, please?
Haag’s Theorem says roughly that (at least in the Wightman axiomatization of QFT) the interaction picture doesn’t exist for relativistic systems with infinitely many degrees of freedom. Nevertheless, the S-matrix (or an adiabatically switched local version of it, to control the infrared divergences) appears to have an asymptotic perturbative expansion in a Weiner-type series *AS IF* the interaction picture from nonrelativistic quantum mechanics held in QFT. The perturbative expansion of the S-matrix in QFT can be motivated by analogy with nonrelativistic QM, but strictly speaking, its existence can’t really be attributed rigorously to the applicability of the interaction picture. Of course, Wightman’s axioms could be very wildly off-base, neutralizing the sting of Haag’s Theorem, but that would leave us even more in the dark as to the rigorous mathematical nature of QFT. Most QFT textbooks sweep this whole issue under the rug by failing even to mention Haag’s Theorem. One standard text (not working in the mathematically rigorous “causal perturbation theory” framework) that is at least refreshingly honest about the issue is Anthony Duncan’s beautiful book, “The Conceptual Framework of Quantum Field Theory”. Thanks for this nice video. Cheers.
I used to make the documents in my videos available to one dollar patrons on patreon, but I stopped doing that because it was a hassle. For now, you will just have to due with the video.
Thanks a lot, your explanations and notes are really more than diamond or gold worthy
Wow, best video on this theme I have found on youtube! Thank you!!
Our QFT reading club will know a lot more about interaction picture now :)
Can you do some videos based on PATH INTEGRAL for qft (i.e. for photon field, fermionic field, scalar field) because I really need help about this over the course of my graduating, please?
Haag’s Theorem says roughly that (at least in the Wightman axiomatization of QFT) the interaction picture doesn’t exist for relativistic systems with infinitely many degrees of freedom. Nevertheless, the S-matrix (or an adiabatically switched local version of it, to control the infrared divergences) appears to have an asymptotic perturbative expansion in a Weiner-type series *AS IF* the interaction picture from nonrelativistic quantum mechanics held in QFT. The perturbative expansion of the S-matrix in QFT can be motivated by analogy with nonrelativistic QM, but strictly speaking, its existence can’t really be attributed rigorously to the applicability of the interaction picture. Of course, Wightman’s axioms could be very wildly off-base, neutralizing the sting of Haag’s Theorem, but that would leave us even more in the dark as to the rigorous mathematical nature of QFT. Most QFT textbooks sweep this whole issue under the rug by failing even to mention Haag’s Theorem. One standard text (not working in the mathematically rigorous “causal perturbation theory” framework) that is at least refreshingly honest about the issue is Anthony Duncan’s beautiful book, “The Conceptual Framework of Quantum Field Theory”.
Thanks for this nice video. Cheers.
Thank you Sir
nice Sir thank you
Sir do you believe that our world is a simulation 🧐btw love from india sir ❤️❤️
I can't understand what is T hear
The time-ordering operator.
@@DietterichLabs does it have explicit value
Amazing!
Hello. Can you provide the document in the video?
I used to make the documents in my videos available to one dollar patrons on patreon, but I stopped doing that because it was a hassle. For now, you will just have to due with the video.
@@DietterichLabs i pause your videos and write down, thank you for the resources you provide. Do you still have patreon?
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