S-matrix

E9111

concept in quantum field theory operator scattering matrix

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.

Try in SPARQL Jump to: Surface forms Statements Referenced by

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

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.

Feynman diagrams → relatedConcept → S-matrix ⓘ

Feynman rules → relatedTo → S-matrix ⓘ

Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED → usesConcept → S-matrix ⓘ

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

Werner Heisenberg → notableWork → S-matrix ⓘ

this entity surface form: S-matrix theory

Gell-Mann–Low theorem → involves → S-matrix ⓘ

LSZ reduction formula → relatedTo → S-matrix ⓘ

Tomonaga–Schwinger equation → relatedTo → S-matrix ⓘ

information loss paradox → involvesConcept → S-matrix ⓘ

Born series → expands → S-matrix ⓘ

this entity surface form: T-matrix

Lippmann–Schwinger equation → relatedTo → S-matrix ⓘ