I've started studying QFT this year and in trying to find a more rigorous approach to the subject I ended up find out lots of people saying that "there is no way known yet to make QFT rigorous when there are interactions".
As for the textbook approach, even without interactions it already seems not much rigorous, still, approaching it in the right way it seems to be possible to make it precise.
Now, the rigour issue with interactions in QFT isn't explained in the books I'm using, and I confess I still didn't get it.
I mean: some people say the problem are the Dyson's series that in QFT wouldn't converge, some people say the issue is that the Fock space representation cannot be built with interactions and hence particles don't even exist in this case. Some people even say that it is not even possible to describe the theory with Hilbert spaces. And there are quite a few more points people make on this matter.
My question here isn't "how to solve these issues" because it seems to me that up to this day no one knows this yet. My question is: what really is the problem in more concrete terms.
What are the problems that make QFT with interactions be non rigorous? How interactions causes these problems in contrast to free QFT?
No comments:
Post a Comment