What physicists mean when they say 1+2+3+... = -1/12pic.twitter.com/Noj5pEf1Ym
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I want to be clear. I do not assert any "equality" of the sum to -1/12 in the limit that ε-->0. This makes no sense What does make sense is to speak about a "finite piece" and a divergent piece. This result is unique, as outlined by Terrance Tao.https://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/ …
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Sometimes in physics, absolute quantities don't have a meaning. Rather what does have a meaning is *differences* . In these situations, the term that *would* diverge cancels out completely leaving behind a finite answer; giving way to the following "replacement rule"pic.twitter.com/QHm3LbXoai
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Wow. DCM again. I have noticed this used in Game Theory, Nash Manifolds and it is even suggestive in Asymptotically Ideal Money. Help an amateur out here. Why?pic.twitter.com/OnDmp9T5f2
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Consider this as intuition. What would happen if we tried to regularize an already-convergent series? Since everything is absolutely convergent, when we take the limit as ε-->0 we can pull it inside the sum which returns the original sum.pic.twitter.com/bm793vUnSK
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Such a cool account! Thanks for sharing this. Ever since I learned to take integrals of real-valued functions through branch cuts to allow them to converge I've been convinced that Complex Analysis is probably the weirdest area of math.
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Apparently Nova needs to do more work in filling the gaps in my incomplete understanding about this. Unfortunately, this along with dozens of HEP books, has to wait a bit. Good to have you guys hanging around.
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Thank you for sharing~
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So it's just an abuse of notation?
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