Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Value of Ramanujan Summation In Quantum Mechanics

+ 0 like - 0 dislike
1059 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 in Mathematics by 4545454545SI (0 points) [ revision history ]
reshown Apr 1, 2014 by dimension10
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

1 Answer

+ 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 Dilaton (6,240 points) [ revision history ]

Your answer

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):
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$\hbar$ys$\varnothing$csOverflow
Then 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




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...