Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
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. – felix Aug 8 '11 at 7:52 here my paper on how can the zeta regularization and Ramanujan resummation be used to get finite values in quantum mechanics – Jose Javier Garcia May 27 '13 at 17:18
up vote 6 down vote accepted

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:

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

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.