Dyson series
E9110
The Dyson series is a perturbative expansion in quantum field theory that expresses time-ordered exponentials and scattering amplitudes as an infinite series of integrals, each term corresponding to a Feynman diagram.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Dyson series in quantum electrodynamics | 3 |
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
concept in quantum field theory
ⓘ
mathematical formalism ⓘ perturbative expansion ⓘ |
| alternativeTo | nonperturbative methods in quantum field theory ⓘ |
| appliesTo |
nonrelativistic quantum mechanics with time-dependent interactions
ⓘ
relativistic quantum field theories ⓘ |
| approximationType | perturbative series in coupling constants ⓘ |
| assumes |
adiabatic switching on and off of interactions
ⓘ
existence of free and interacting field decomposition ⓘ |
| basedOn |
interaction picture of quantum mechanics
ⓘ
time-dependent perturbation theory ⓘ |
| clarifiedBy | operator formalism of quantum field theory ⓘ |
| convergenceProperty | typically asymptotic rather than convergent ⓘ |
| correspondsTo |
infinite series of time-ordered integrals
ⓘ
sum over Feynman diagrams ⓘ |
| describes |
scattering amplitudes
ⓘ
time evolution operator in the interaction picture ⓘ time-ordered exponential of the interaction Hamiltonian ⓘ |
| expands |
S-matrix operator
ⓘ
time evolution operator in interaction picture ⓘ time-ordered exponential operator ⓘ |
| field |
quantum field theory
ⓘ
theoretical physics ⓘ |
| hasComponent |
interaction Hamiltonian density
ⓘ
time-ordered products of interaction terms ⓘ time-ordering operator ⓘ |
| historicalDevelopment | formulated by Freeman Dyson in the late 1940s ⓘ |
| limitation |
breaks down at strong coupling
ⓘ
may be non-convergent but asymptotic ⓘ |
| mathematicalForm | infinite sum of multiple time integrals ⓘ |
| namedAfter | Freeman Dyson ⓘ |
| relatedTo |
Feynman diagrams
ⓘ
Gell-Mann–Low theorem ⓘ S-matrix ⓘ Wick’s theorem ⓘ
surface form:
Wick's theorem
path integral formulation ⓘ time-ordered products ⓘ |
| requires | time-ordering of interaction operators ⓘ |
| termCorrespondsTo |
Feynman diagram with n interaction vertices
ⓘ
n-th order perturbation in the coupling constant ⓘ |
| usedFor |
derivation of Feynman diagram rules
ⓘ
perturbative calculation of S-matrix elements ⓘ systematic expansion in powers of the interaction coupling constant ⓘ |
| usedIn |
perturbative quantum chromodynamics
ⓘ
quantum electrodynamics ⓘ standard model calculations ⓘ |
Referenced by (9)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Dyson series in quantum electrodynamics
subject surface form:
Freeman Dyson
this entity surface form:
Dyson series in quantum electrodynamics
subject surface form:
Freeman Dyson
this entity surface form:
Dyson series in quantum electrodynamics