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.
Aliases (5)
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
formulation of quantum mechanics
→
path integral formulation → quantum theory formalism → |
| alsoKnownAs |
Feynman sum-over-paths
→
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 → |
| 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
→
Hamiltonian path integral → Wick rotation → 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)
→
|
Referenced by (6)
| Subject (surface form when different) | Predicate |
|---|---|
|
Feynman path integral
("Feynman sum-over-paths")
→
|
alsoKnownAs |
|
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
("Feynman formulation of QED")
→
|
demonstratesEquivalenceOf |
|
The Grand Design
("Feynman path integral formulation")
→
|
explains |
|
The Universe in a Nutshell
("Feynman path integrals")
→
|
explainsConcept |
|
Feynman checkerboard model
→
|
relatedTo |
|
quantum field theory
("path integral formulation")
→
|
usesConcept |