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- Functional_integration abstract "Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space, but a space of functions. Functional integrals arise in probability, in the study of partial differential equations, and in the path integral approach to the quantum mechanics of particles and fields.In an 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 P. J. Daniell in a paper of 1919 and N. Wiener in a series of studies culminating in his papers of 1921 on Brownian motion. They developed a rigorous method (now known as the Wiener measure) for assigning a probability to a particle's random path. R. Feynman developed another functional integral, the path integral, useful for computing the quantum properties of systems. In Feynman's path integral, the classical notion of a unique trajectory for a particle is replaced by an infinite sum of classical paths, each weighted differently according to its classical properties.Functional integration is central to quantization techniques in theoretical physics. The algebraic properties of functional integrals are used to develop series used to calculate properties in quantum electrodynamics and the standard model of particle physics.".
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- Functional_integration wikiPageWikiLink Brownian_motion.
- Functional_integration wikiPageWikiLink Category:Functional_analysis.
- Functional_integration wikiPageWikiLink Category:Integral_calculus.
- Functional_integration wikiPageWikiLink Category:Mathematical_physics.
- Functional_integration wikiPageWikiLink Category:Quantum_field_theory.
- Functional_integration wikiPageWikiLink Category:Quantum_mechanics.
- Functional_integration wikiPageWikiLink Domain_of_a_function.
- Functional_integration wikiPageWikiLink Fermion.
- Functional_integration wikiPageWikiLink Fractional_Schrödinger_equation.
- Functional_integration wikiPageWikiLink Fractional_quantum_mechanics.
- Functional_integration wikiPageWikiLink Fractional_statistical_mechanics.
- Functional_integration wikiPageWikiLink Function_space.
- Functional_integration wikiPageWikiLink Functional_(mathematics).
- Functional_integration wikiPageWikiLink Functional_integration_(neurobiology).
- Functional_integration wikiPageWikiLink Gaussian_integral.
- Functional_integration wikiPageWikiLink Grassmann_number.
- Functional_integration wikiPageWikiLink Hagen_Kleinert.
- Functional_integration wikiPageWikiLink Integral.
- Functional_integration wikiPageWikiLink Lebesgue_integration.
- Functional_integration wikiPageWikiLink Lie_product_formula.
- Functional_integration wikiPageWikiLink Lévy_process.
- Functional_integration wikiPageWikiLink Manifold.
- Functional_integration wikiPageWikiLink Mathematics.
- Functional_integration wikiPageWikiLink Measure_(mathematics).
- Functional_integration wikiPageWikiLink Method_of_steepest_descent.
- Functional_integration wikiPageWikiLink Norbert_Wiener.
- Functional_integration wikiPageWikiLink Normal_distribution.
- Functional_integration wikiPageWikiLink Partial_differential_equation.
- Functional_integration wikiPageWikiLink Partition_function_(quantum_field_theory).
- Functional_integration wikiPageWikiLink Path_integral_formulation.
- Functional_integration wikiPageWikiLink Percy_John_Daniell.
- Functional_integration wikiPageWikiLink Perturbation_theory.
- Functional_integration wikiPageWikiLink Physics.
- Functional_integration wikiPageWikiLink Probability.
- Functional_integration wikiPageWikiLink Quantum_electrodynamics.
- Functional_integration wikiPageWikiLink Quantum_mechanics.
- Functional_integration wikiPageWikiLink Quotient.
- Functional_integration wikiPageWikiLink Richard_Feynman.
- Functional_integration wikiPageWikiLink Standard_Model.
- Functional_integration wikiPageWikiLink Variance.
- Functional_integration wikiPageWikiLink Wiener_process.
- Functional_integration wikiPageWikiLinkText "Feynman integration".
- Functional_integration wikiPageWikiLinkText "Functional integration".
- Functional_integration wikiPageWikiLinkText "connectivity".
- Functional_integration wikiPageWikiLinkText "functional integral methods".
- Functional_integration wikiPageWikiLinkText "functional integral".
- Functional_integration wikiPageWikiLinkText "functional integrals".
- Functional_integration wikiPageWikiLinkText "functional integration".
- Functional_integration wikiPageWikiLinkText "path integral".
- Functional_integration wikiPageWikiLinkText "path integrals".
- Functional_integration wikiPageUsesTemplate Template:Cite_journal.
- Functional_integration wikiPageUsesTemplate Template:Confusing.
- Functional_integration wikiPageUsesTemplate Template:Expand_section.
- Functional_integration wikiPageUsesTemplate Template:Hatnote.
- Functional_integration wikiPageUsesTemplate Template:Reflist.
- Functional_integration subject Category:Functional_analysis.
- Functional_integration subject Category:Integral_calculus.
- Functional_integration subject Category:Mathematical_physics.
- Functional_integration subject Category:Quantum_field_theory.
- Functional_integration subject Category:Quantum_mechanics.
- Functional_integration hypernym Collection.
- Functional_integration type Book.
- Functional_integration type Function.
- Functional_integration type Mechanic.
- Functional_integration type Physic.
- Functional_integration comment "Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space, but a space of functions.".
- Functional_integration label "Functional integration".
- Functional_integration sameAs Q2450135.
- Functional_integration sameAs Integrale_funzionale.
- Functional_integration sameAs m.01ryxp.
- Functional_integration sameAs Функциональный_интеграл.
- Functional_integration sameAs Q2450135.
- Functional_integration wasDerivedFrom Functional_integration?oldid=678231275.
- Functional_integration isPrimaryTopicOf Functional_integration.