6k views

### 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/...
1k views

### Critical Dimension of Bosonic Strings and Regularization of $\sum_{n=1}^\infty n$

If $D$ is critical dimension of Bosonic strings, a particular derivation goes like the following, where we arrive finally at $$\frac{D-2}{2}\sum_{n=1}^\infty n + 1 = 0.$$ Now mathematically this is ...
418 views

### can we PHYSCALLY (not by mathematics) justify that $\zeta (-s)= 1+2^{s}+3^{s}+4^{s}+…$
the values $\zeta (-1)= -1/12$ and $\zeta (-3)= 1/120$ give accurate results for casimir and to evaluate the dimension in bosonic string theory so is there a physcial JUSTIFICATION to justify ...