Feynman path integral
E21993
The Feynman path integral is a formulation of quantum mechanics in which a particle’s behavior is described as a sum over all possible paths it can take, each weighted by a phase factor derived from the classical action.
All labels observed (8)
How this entity was disambiguated
This entity first appeared as the object of triple T173582 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Feynman path integral Context triple: [Feynman checkerboard model, relatedTo, Feynman path integral]
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A.
Feynman checkerboard model
The Feynman checkerboard model is a path-integral-based lattice model introduced by Richard Feynman to illustrate and derive the behavior of relativistic quantum particles, particularly the Dirac equation in one spatial dimension.
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B.
Feynman diagrams
Feynman diagrams are graphical representations used in quantum field theory to visualize and calculate particle interactions and processes.
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C.
Euclidean quantum field theory
Euclidean quantum field theory is a formulation of quantum field theory in imaginary (Euclidean) time that enables rigorous mathematical treatment and path-integral representations closely connected to statistical mechanics.
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D.
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED is a landmark theoretical result that rigorously demonstrated the mathematical consistency and mutual compatibility of different approaches to quantum electrodynamics.
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E.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Feynman path integral Target entity description: The Feynman path integral is a formulation of quantum mechanics in which a particle’s behavior is described as a sum over all possible paths it can take, each weighted by a phase factor derived from the classical action.
-
A.
Feynman checkerboard model
The Feynman checkerboard model is a path-integral-based lattice model introduced by Richard Feynman to illustrate and derive the behavior of relativistic quantum particles, particularly the Dirac equation in one spatial dimension.
-
B.
Feynman diagrams
Feynman diagrams are graphical representations used in quantum field theory to visualize and calculate particle interactions and processes.
-
C.
Euclidean quantum field theory
Euclidean quantum field theory is a formulation of quantum field theory in imaginary (Euclidean) time that enables rigorous mathematical treatment and path-integral representations closely connected to statistical mechanics.
-
D.
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED is a landmark theoretical result that rigorously demonstrated the mathematical consistency and mutual compatibility of different approaches to quantum electrodynamics.
-
E.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
formulation of quantum mechanics
ⓘ
path integral formulation ⓘ quantum theory formalism ⓘ |
| alsoKnownAs |
Feynman sum-over-paths
ⓘ
linked to:
Feynman path integral
sum-over-histories formulation ⓘ |
| appliesTo |
nonrelativistic quantum mechanics
ⓘ
quantum statistical mechanics ⓘ relativistic quantum field theory ⓘ statistical field theory ⓘ |
| basedOn | principle of least action ⓘ |
| describes | quantum evolution as a sum over all possible paths ⓘ |
| domain |
mathematical physics
ⓘ
theoretical physics ⓘ |
| equivalentTo |
Heisenberg operator formulation of quantum mechanics
ⓘ
Schrödinger formulation of quantum mechanics ⓘ
linked to:
matrix mechanics
|
| generalizes | classical action principle ⓘ |
| hasIssue | mathematical rigor of the path integral measure ⓘ |
| historicallyDevelopedBy | Richard Feynman ⓘ |
| influenced |
modern quantum field theory
ⓘ
string theory ⓘ topological quantum field theory ⓘ |
| introducedInContext | quantum electrodynamics ⓘ |
| mathematicallyFormulatedAs | integral over all paths weighted by exp(iS/ħ) ⓘ |
| namedAfter | Richard Feynman ⓘ |
| relatedTo |
Euclidean path integral
ⓘ
linked to:
Euclidean quantum field theory
Hamiltonian path integral ⓘ Wick rotation ⓘ
linked to:
Euclidean quantum field theory
canonical quantization ⓘ |
| requires | measure over path space ⓘ |
| usedFor |
Euclidean quantum field theory
ⓘ
deriving Feynman rules ⓘ deriving propagators ⓘ instantons and tunneling calculations ⓘ lattice gauge theory formulations ⓘ perturbation theory in quantum field theory ⓘ quantization of gauge theories ⓘ semiclassical approximations ⓘ |
| usedIn |
derivation of Feynman diagrams
ⓘ
path integral Monte Carlo methods ⓘ |
| usesConcept |
Green’s function
ⓘ
Lagrangian ⓘ classical action ⓘ functional integral ⓘ path in configuration space ⓘ phase factor ⓘ propagator ⓘ |
| weightFactor | exp(iS/ħ) ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Feynman path integral Description of subject: The Feynman path integral is a formulation of quantum mechanics in which a particle’s behavior is described as a sum over all possible paths it can take, each weighted by a phase factor derived from the classical action.
Referenced by (9)
Full triples — surface form annotated when it differs from this entity's canonical label.
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
→
demonstratesEquivalenceOf
→
Feynman formulation of QED
ⓘ
linked to: Feynman path integral
linked to: Feynman path integral
linked to: Feynman path integral
linked to: Feynman path integral
linked to: Feynman path integral
linked to: Feynman path integral
Schrödinger formulation of quantum mechanics
→
relatedConcept
→
path integral formulation of quantum mechanics
ⓘ
linked to: Feynman path integral
linked to: Feynman path integral