# Value of Ramanujan Summation In Quantum Mechanics

+ 0 like - 0 dislike
1388 views

In mathematics, sum of all natural number is infinity.

but Ramanujan suggests whole new definition of summation.

"The sum of $n$ is $-1/12$" what so called Ramanujan Summation.

First he find the sum, only Hardy recognized the value of the summation.

And also in quantum mechanics(I know), Ramanujan summation is very important.

Question. What is the value of Ramanujan summation in quantum mechanics?

This post imported from StackExchange Physics at 2014-03-17 04:00 (UCT), posted by SE-user 4545454545SI

asked Aug 8, 2011
reshown Apr 1, 2014
What's the value of the golden ratio in Newtonian mechanics? What's the value of 1+1/2+1/4+1/8+... in general relativity? You're mixing up math with unrelated physics.

This post imported from StackExchange Physics at 2014-03-17 04:00 (UCT), posted by SE-user felix
vixra.org/abs/1003.0235 here my paper on how can the zeta regularization and Ramanujan resummation be used to get finite values in quantum mechanics

This post imported from StackExchange Physics at 2014-03-17 04:00 (UCT), posted by SE-user Jose Javier Garcia

+ 6 like - 0 dislike

Lumo gives a very nice step by step calculation of this sum and a good discussion of the importance and application of such summation techniques in QFTs here:

http://motls.blogspot.com/2011/07/why-is-sum-of-integers-equal-to-112.html

Such mathematical calculations are NOT unrelated to physics; on the contrary they are important...

answered Aug 8, 2011 by (6,240 points)

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$y$\varnothing$icsOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). Please complete the anti-spam verification