So I'm interested in formally asking if this question to collect examples of divergent series in physics can be opened:
There are examples of this that come up in QFT and I found one example closer to Chemistry but there's not single resource which covers all such examples.
The question got closed (very reasonably) because as it stands its asking for a list and needs to at least be vetted the meta.
So I'm sure there might be a couple questions about "why should we allow this?" and I'll address them as best as I can.
"It's just a list, its not about conceptual physics and might even attract low quality answers" This question actually elicits a good amount of conceptual physics and is therefore on topic. The way I want the list to be structured is to strictly contain new examples along with where the example came from without repeats. So every addition to this (I'm planning on making a community wiki answer) will necessarily be linking a new piece of conceptual physics along with a divergent series. The fact I have already mentioned the casimir effect/riemann zeta function means that this low hanging fruit is no longer available for an answer and so that ensures we have some quality control/easy ability to prevent pointless/repeated answers. Moreover this question is NOT an opinion based question. You either have a new example that isn't already documented or you don't and that example either is a real calculation from some part of physics (possibly purely theoretical) or it consists of invalid math/incorrect modelling. So we can definitely ensure the quality will be high
"But if we give an exception here what about other exceptions, why not a list of type ___ while we are at it, where do we draw the line?" I don't know where to draw the line and I'm not asking meta the hard question of what that explicit line should be. If someone cares about __ topic enough they can just ask on meta and test the reception for themselves, just like I'm doing here. I do know that I care about divergent series, and I think there other people who do care too, and so I am asking about this specific topic which I find interesting and is linked to a lot of interesting physics .
"Maybe you're the only person that cares about this?" This question is interesting to more than just myself, divergent series appear in pure mathematics (such as number theory and complex analysis) and people from that space (such as myself) would probably be curious where and how divergent series appear in physics. Here is a post from mathoverflow setting up a small such table: https://mathoverflow.net/q/401386/ moreover a quick check on the search bar reveals many questions about divergent series have popped up in the past on physics.stackexchange
"If we make this exception, we will be flooded with requests that we cannot sustain" I did some research for an answer here and found that mathoverflow which is a considerably smaller site is able to allow the occasional list/table without being overwhelmed so I think allowing this list to form (once its vetted and debated on meta) will not overwhelm physics.stackexchange.com
"But the rules/norms are already set. We shouldn't be making exceptions" I like the answer of Chiral Anomaly here which tries to explore what the purpose of physics.stackexchange MIGHT be. The post there addresses that the core value add should be to organize questions and answers that are useful, of high quality, and easily found by others. I think that I've addressed the first two points but the last point is key, asking it HERE on physics.stackexchange would make it very EASILY found by others compared to using any other resource/place. So I believe this is a good home for this list.
I'm not sure if that covers everything but it hopefully addresses some concerns.
Please let me know what changes/modifications/upgrades to the question you would like to see to make you feel comfortable about it being posted on the main site.