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This question is primarily mathematical in nature. I have been reading Quantum Field Theory for the Gifted Amateur and I am reading about Feynman’s path integral approach. The definition of the “sum over all paths integral” is given as including a capital pi symbol. For example,

enter image description here

I am familiar with the pi function as a modified gamma function and an extension of the factorial system, but I have never seen it listed with limits. If someone could explain the meaning of this notation or provide an alternate working definition of this integral, I would greatly appreciate.

(the image is not from the book, but it includes the pi symbol I am interested in)

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    $\begingroup$ The capital pi means a product, just like capital sigma means a sum. Just as $\sum_{i=1}^3 i = 1 + 2 + 3$, $\prod_{i=1}^3 i = 1 * 2 * 3$. $\endgroup$ – knzhou Jun 27 '20 at 19:10
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$\prod_{j=1}^\infty$ means a product of what follows, with the factors having $j=1,2,3,\dots$. In this case there are an infinite number of factors so this is called an infinite product. Infinite products can converge or diverge, just like infinite sums.

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  • $\begingroup$ Thank you so much, not as hard as I thought $\endgroup$ – Stoby Jun 28 '20 at 2:04

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