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Everything about Functional integration
Integration over the space of functions
Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer an ordinary region of space, but a space of functions. Functional integrals appear in probability, in the study of partial differential equations, and in the path integral formulation to the quantum mechanics of particles and fields. While the term suggests an extension of ordinary integration, the lack of a translation-invariant measure on infinite-dimensional spaces means that functional integrals must be defined by more subtle methods or interpreted formally. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Functional integrationA 5-minute orientation
- Skim a recent paper: Integrated Sensing and Communications: Toward Dual-Functional Wireless Networks for 6G and BeyondInfluential work since 2022
- Pick up a classic book: The integration of functions of a single variableThe most-reprinted book on the subject
- Read the landmark paper: Functional Integration of Adult-Born NeuronsCited 240 times
- Go sideways: Path-integral formulationA closely related topic
- Go sideways: Feynman–Kac formulaA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Functional Integration of Adult-Born Neurons
Supersymmetry and functional integration measures
Functional determinants by contour integration methods
Cross‐functional integration and functional coordination in purchasing and supply management
Functional integration over geometries
Functional integration and the mind
State-related functional integration and functional segregation brain networks in schizophrenia
Coping with functional collective action dilemma: functional fragmentation and administrative integration
🆕 Influential since 2022
Integrated Sensing and Communications: Toward Dual-Functional Wireless Networks for 6G and Beyond
MicrobiomeAnalyst 2.0: comprehensive statistical, functional and integrative analysis of microbiome data
Toward Multi-Functional 6G Wireless Networks: Integrating Sensing, Communication, and Security
A microfluidic platform integrating functional vascularized organoids-on-chip
📚 Books worth reading
The integration of functions of a single variableG. H. Hardy, J. G. Leathem · 1905
Complex integration and Cauchy's theoremG. N. Watson · 1914
Traité d'analyseEmile Picard · 1891
Cours d'analyse de l'École polytechniqueCamille Jordan · 1882
Functional IntegrationPierre Cartier, Cecile DeWitt-Morette · 1995
Théorie de l'intégraleS. Saks · 1933
Elements of the integral calculusByerly, William Elwood · 1881
Quantum many-particle systemsJohn W. Negele · 1988
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Partition function (quantum field theory) In quantum field theory, partition functions are generating functionals for correlation functions, making them key objects of study in the path integral…
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