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.
All labels observed (4)
| Label | Occurrences |
|---|---|
| S-matrix canonical | 8 |
| Dyson’s papers on the S-matrix in quantum electrodynamics | 1 |
| S-matrix theory | 1 |
| T-matrix | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T100551 — 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: S-matrix Context triple: [Feynman diagrams, relatedConcept, S-matrix]
-
A.
Feynman diagrams
Feynman diagrams are graphical representations used in quantum field theory to visualize and calculate particle interactions and processes.
-
B.
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.
-
C.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
-
D.
Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
-
E.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
- 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: S-matrix Target entity description: 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.
-
A.
Feynman diagrams
Feynman diagrams are graphical representations used in quantum field theory to visualize and calculate particle interactions and processes.
-
B.
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.
-
C.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
-
D.
Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
-
E.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
- F. None of above. chosen
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 ⓘ |
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: S-matrix Description of subject: 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.
Referenced by (11)
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
→
relatedWork
→
S-matrix
ⓘ
this entity surface form:
Dyson’s papers on the S-matrix in quantum electrodynamics
this entity surface form:
S-matrix theory
this entity surface form:
T-matrix