While reading a paper I saw the following integral equation.

$$\frac{1}{g} = \int_{-\pi}^{\pi} (\prod_{\sigma}\frac{\mathrm{d}p_{\sigma}}{2\pi}) \frac{\delta(\Sigma_{\sigma} p_{\sigma})}{(\prod_{\sigma} (1+\frac{2 \mathrm{sin}(p_{\sigma}/2)}{m}) -1)} \, ,\, \mathrm{with}\, \sigma = {1,2,3,4} $$

But there was no solution given for it. To learn more about this integral equation, I would like to solve it. Sadly I don't even know how to begin/deal with this equation or more precisely with the integral itself. Hopefully someone can give me a hint or two.


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  • $\begingroup$ Does the equation somehow tie in with physics? If not you might want to reconsider and post this to the Mathematics stack exchange. Sorry I can't help you, but you might want to check out Paul Nahin's new book "Inside Interesting Integrals". He has lots of good tips, tricks for solving definite integrals. Good luck! $\endgroup$ – docscience Apr 29 '15 at 13:54
  • $\begingroup$ The paper is about non-relativistic fermions (in two dimensional euclidean space-time) and with this integral one should be able to determine the coupling g. Thanks for the book recommendation - I will check it out! $\endgroup$ – nerdizzle Apr 29 '15 at 14:04
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    $\begingroup$ Maybe you could add a definition for each symbol. This can help others to find a solution to your problem. For example, what is delta in your case? $\endgroup$ – sagittarius_a Apr 29 '15 at 14:47
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    $\begingroup$ $\uparrow$ Which paper? $\endgroup$ – Qmechanic Apr 29 '15 at 16:24
  • $\begingroup$ But there was no solution given for it. The equal sign suggests that the solution is $\frac1g$, no? Why was it not solved in the paper? Does it even make sense to solve it? $\endgroup$ – Name Apr 29 '15 at 16:34

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