Revision as of 09:50, 28 April 2020 edit Tea2min (talk \| contribs) Extended confirmed users, Pending changes reviewers 21,975 edits Remove one submarine link. I think linking the text "region of space" to manifold here is more confusing than helpful. Of course, feel free to revert if you disagree. ← Previous edit		Revision as of 09:53, 28 April 2020 edit undo Tea2min (talk \| contribs) Extended confirmed users, Pending changes reviewers 21,975 edits →top: Minor rewording to make link to Lebesgue integration more obvious. Next edit →
Line 3: '''Functional integration''' is a collection of results in [[mathematics]] and [[physics]] where the [[___domain (mathematics)\|___domain]] of an [[integral]] is no longer a region of space, but a [[Function space\|space of functions]]. Functional integrals arise in [[probability]], in the study of [[partial differential equations]], and in the [[path integral formulation\|path integral approach]] to the [[quantum mechanics]] of particles and fields. In an ordinary integral (in the sense of [[Lebesgue integration~~\|ordinary integral~~]]) there is a function to be integrated (the integrand) and a region of space over which to integrate the function (the ___domain of integration). The process of integration consists of adding up the values of the integrand for each point of the ___domain of integration. Making this procedure rigorous requires a limiting procedure, where the ___domain of integration is divided into smaller and smaller regions. For each small region, the value of the integrand cannot vary much, so it may be replaced by a single value. In a functional integral the ___domain of integration is a space of functions. For each function, the integrand returns a value to add up. Making this procedure rigorous poses challenges that continue to be topics of current research. Functional integration was developed by [[Percy John Daniell]] in an article of 1919<ref>{{Cite journal

Functional integration: Difference between revisions