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Where is sum of divergent series and values of divergent integrals used in physics?

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Hello everyone!

My question is:

Where is sum of divergent series and divergent integrals used in physics? What it all means? Where can I find examples of divergent integrals? Is there a book of problems for physicists?

I am mathematician. I developed a method for summing divergent series and determines the value of divergent integrals https://m4t3m4t1k4.wordpress.com/2015/02/14/general-method-for-summing-divergent-series-determination-of-limits-of-divergent-sequences-and-functions-in-singular-points-v2/ I am fascinated by the time they have the application in physics. What is the point of it all? How to interpret all physicists? Also looking for examples of divergent integrals to challenge that method. So far I've found three examples that I have tested in the work.

Thanx.

Closed as per community consensus as the post is undergraduate-level

asked Feb 17, 2015 in Closed Questions by Sinisa [ no revision ]
retagged Nov 26, 2015 by dimension10

Cross-posted to Physics.SE and PhysicsForums.

The paragraph linking to some blog post doesn't seem relevant to the rest of the post (and probably a bad attempt at self-promotion).

commented Feb 18, 2015 by dimension10 (1,985 points) [ no revision ]
edited Feb 18, 2015 by dimension10

This is undergraduate-level, voting to close.

commented Feb 18, 2015 by dimension10 (1,985 points) [ no revision ]

Voting to close.

commented Feb 18, 2015 by Vladimir Kalitvianski (102 points) [ no revision ]

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1 Answer

Path integrals are an obvious example - perturbation series are often divergent sums. Renormalisation is all about getting rid of these infinities. For example, the Ramanujan sum is encountered rather frequently in QFT and string theory, $\varepsilon = \sum_{n=0}^\infty n := -1/12$ , represents the Casimir energy in string theory, for example.

answered Feb 18, 2015 by dimension10 (1,985 points) [ revision history ]

Thanx dimension10. Where can I find examples of divergent integrals? Is there a book of problems for physicists?

commented Feb 18, 2015 by sinisa [ no revision ]

@sinisa Do a simple web search, keywords "perturbation series", "renormalisation", "ramanujan sums qft", etc. There are lots of them.

commented Feb 18, 2015 by dimension10 (1,985 points) [ no revision ]

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