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### How does the sum of the series “1 + 2 + 3 + 4 + 5 + 6…” to infinity = “-1/12”? [duplicate]

How does the sum of the series “1 + 2 + 3 + 4 + 5 + 6…” to infinity = “-1/12”, in the context of physics? I heard Lawrence Krauss say this once during a debate with Hamza Tzortzis (http://youtu.be/...
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### What areas of physics depend on the sum $1 + 2 + 3 + 4 + 5 + 6+ 7+\ldots= -1/12$? [duplicate]

This youtube video from Numberphile, http://youtu.be/w-I6XTVZXww shows how the value is derived. In the video, one interviewee claims that "this result is used in many areas of physics". In the video,...
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### $\zeta(-1)=\frac{-1}{12}\nRightarrow \sum_\limits{i=1}^\infty i=\frac{-1}{12}$ so how do we justify its use in string theory? [duplicate]

I asked math.stackexchange about my concerns regarding the justification of the claim that $1+2+3+...=\frac{-1}{12}$ Once you have defined $\zeta(s) =\sum_\limits{n=1}^\infty\frac{1}{n^s}$ ...
87 views

### Why string theorist use the following result? [duplicate]

$1+2+3.......$so on $= -1/12.$ I have seen a few proofs of this result. And I hope most of you are familiar with them. Why string theorist use this ambiguous result in string theory, when assigning ...
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### Regularization of the Casimir effect

For starters, let me say that although the Casimir effect is standard textbook stuff, the only QFT textbook I have in reach is Weinberg and he doesn't discuss it. So the only source I currently have ...
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### What is the relation between renormalization in physics and divergent series in mathematics?

The theory of Divergent Series was developed by Hardy and other mathematicians in the first half of the past century, giving rigorous methods of summation to get unique and consistent results from ...
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### What is the reason/significance of using $\sum\limits_{n=1}^{\infty}n\rightarrow-\frac{1}{12}$?

What is the reason/significance of using a trick equation in the Volume I - String Theory - Joseph Polchinsky? I have no doubts at all that the author knows extremely well the subject and that this ...
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### Pedagogical explanations of critical dimensions of string theories

Once you understand the formalism, I think it's clearest to say the critical dimension of the space-time arises because we need to cancel the central charge of the (super)conformal ghosts on the ...
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### Is the fact that the sum of all natural numbers $\sum_{n=1}^\infty n = -\frac{1}{12}$ essential to the understanding of the Casimir Force In QED?

Apparently this result is used in many areas physics including the extra dimensions of string theory, which is not the scope of the question. The result is apparently also used to understand the ...
447 views

### Divergent sum in lightcone quantization of bosonic string theory

I had the following question regarding lightcone quantization of bosonic strings - The normal ordering requirement of quantization gives us this infinite sum $\sum_{n=1}^\infty n$. This is regularized ...
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### Have experiments ever suggested two different values to the same divergent series?

I believe to have understood that some physical experiments suggest finite values to divergent series (please correct me if I'm wrong, my understanding of these matters is limited). I heard, for ...
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### Where and how exactly does string theory and Q.E.D. use zeta function regularization?

In the video they mention it being used in many fields of physics inclusing String and QED theory. https://www.youtube.com/watch?v=w-I6XTVZXww But I remember reading somewhere that 1+2+3..=-1/12 is ...
I am trying to derive the quantum form of the Virasoro constraints. $$L_{m} = \frac{1}{2} \sum_{n} :\alpha_{m-n}.\alpha_{n}:$$ :...: meaans normal ordering. Using the common commutator between ...