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Apr 18, 2017 at 9:12 comment added FraSchelle @AccidentalFourierTransform Indeed, I didn't wanted to enter too much details, feel free to post your own answer to complete mine. I had the feeling my answer gently introduces the concept of perturbation series. It seems the OP never opened a book on QFT so I just gave handwaving arguments.
Apr 18, 2017 at 9:11 comment added FraSchelle @annav Indeed, I completely forget renormalisation, thanks for pointing this out. It's a shame indeed. Feel free to complete my answer. I had the feeling my answer gently introduces the concept of perturbation series. It seems the OP never opened a book on QFT so I just gave handwaving arguments.
Apr 18, 2017 at 8:50 comment added AccidentalFourierTransform IMHO, this answer completely neglects the nature of asymptotic series, which are the core of the question. Also, the claims about "physicists being unable to do things rigorously" is completely unjustified.
Apr 18, 2017 at 8:48 comment added anna v where does renormalization enter in this argumetn? I thought it was invented in order to avoid the infinities. Is it a different story? see physics.umd.edu/courses/Phys851/Luty/notes/renorm.pdf
Apr 18, 2017 at 8:43 history answered FraSchelle CC BY-SA 3.0