What physicists mean when they say 1+2+3+... = -1/12pic.twitter.com/Noj5pEf1Ym
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I find this really not convincing. It feels like you just saying S= -1/12 + \infty. But for any constant A you could write S=A+\infty so I don’t see what’s special about -1/12. I find the analytic continuation explanation much more convincing. Unless I’m missing something here?
The limit is never actually taken to zero. The 1/ε^2 actually tells us precisely about the pole structure of the function. There is no assertion about an "equality" when ε-> 0. It does however, make sense to speak about a "convergent piece" and divergent piece in this limit.
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the answer is unique, and is independent of renormalization scheme as outlined in Terrance Tao's post
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