S-matrix
E9111
The S-matrix (scattering matrix) is a fundamental construct in quantum field theory that encodes the probabilities for transitions between initial and final particle states in scattering processes.
Observed surface forms (2)
| Surface form | Occurrences |
|---|---|
| Dyson’s papers on the S-matrix in quantum electrodynamics | 1 |
| S-matrix theory | 1 |
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
concept in quantum field theory
ⓘ
operator ⓘ scattering matrix ⓘ |
| actsOn | asymptotic particle states ⓘ |
| appearsIn |
Standard Model
ⓘ
surface form:
standard model of particle physics
string theory scattering computations ⓘ |
| assumes | existence of asymptotic free states ⓘ |
| codomain | Hilbert space of asymptotic states ⓘ |
| computedUsing |
Dyson series
ⓘ
perturbation theory ⓘ time-ordered exponentials ⓘ |
| constraint |
analyticity in complex energy and momentum variables
ⓘ
cluster decomposition principle ⓘ crossing symmetry (in many relativistic theories) ⓘ |
| dependsOn | interaction Hamiltonian ⓘ |
| domain | Hilbert space of asymptotic states ⓘ |
| elementType | complex numbers ⓘ |
| encodes |
probabilities for scattering processes
ⓘ
transition amplitudes ⓘ |
| field |
quantum field theory
ⓘ
scattering theory ⓘ |
| formalDefinition | S = 1 + iT ⓘ |
| hasElement |
decay amplitudes
ⓘ
elastic scattering amplitudes ⓘ inelastic scattering amplitudes ⓘ particle production amplitudes ⓘ |
| historicalContext | central object in the S-matrix program of the 1950s–1960s ⓘ |
| maps | in-states to out-states ⓘ |
| mathematicalNature | infinite-dimensional matrix in general ⓘ |
| matrixElementNotation | S_{fi} = ⟨f|S|i⟩ ⓘ |
| probabilityRelation | P_{i→f} = |S_{fi}|^2 ⓘ |
| property |
Lorentz invariant (in relativistic QFT)
ⓘ
causal (consistent with microcausality) ⓘ unitary (S†S = 1) ⓘ |
| relatedConcept |
Feynman diagrams
ⓘ
LSZ reduction formula ⓘ T-matrix ⓘ cross section ⓘ optical theorem ⓘ scattering amplitude ⓘ unitarity ⓘ |
| relates | initial states to final states ⓘ |
| representation |
in momentum space
ⓘ
in partial waves ⓘ |
| symmetryConstraint |
Poincaré invariance
ⓘ
internal symmetries of the theory ⓘ |
| usedFor |
computing decay rates
ⓘ
predicting experimental scattering cross sections ⓘ testing quantum field theories against experiment ⓘ |
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
S-matrix theory
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
→
relatedWork
→
S-matrix
ⓘ
this entity surface form:
Dyson’s papers on the S-matrix in quantum electrodynamics