Dyson’s formula
E284667
Dyson’s formula is a key expression in quantum field theory that provides the perturbative expansion of time-ordered exponentials, forming the basis of the Dyson series used to compute interaction effects.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Dyson’s formula canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2631114 — 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: Dyson’s formula Context triple: [Gell-Mann–Low theorem, relatedTo, Dyson’s formula]
-
A.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
B.
Dynkin formula
Dynkin formula is a fundamental result in the theory of Markov processes that expresses the expected value of a function of the process at a stopping time in terms of its generator and an integral over time.
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C.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
D.
Kubo formula
The Kubo formula is a fundamental result in linear response theory that expresses transport coefficients and response functions in terms of equilibrium correlation functions in statistical mechanics and quantum many-body physics.
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E.
Chapman–Kolmogorov equation
The Chapman–Kolmogorov equation is a fundamental relation in the theory of stochastic processes that expresses how transition probabilities of a Markov process over longer time intervals can be obtained by integrating over intermediate states.
- 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: Dyson’s formula Target entity description: Dyson’s formula is a key expression in quantum field theory that provides the perturbative expansion of time-ordered exponentials, forming the basis of the Dyson series used to compute interaction effects.
-
A.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
B.
Dynkin formula
Dynkin formula is a fundamental result in the theory of Markov processes that expresses the expected value of a function of the process at a stopping time in terms of its generator and an integral over time.
-
C.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
D.
Kubo formula
The Kubo formula is a fundamental result in linear response theory that expresses transport coefficients and response functions in terms of equilibrium correlation functions in statistical mechanics and quantum many-body physics.
-
E.
Chapman–Kolmogorov equation
The Chapman–Kolmogorov equation is a fundamental relation in the theory of stochastic processes that expresses how transition probabilities of a Markov process over longer time intervals can be obtained by integrating over intermediate states.
- F. None of above. chosen
Statements (31)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical formula
ⓘ
result in quantum field theory ⓘ |
| appliesTo | time-ordered exponentials of interaction Hamiltonians ⓘ |
| assumes |
existence of an interaction picture
ⓘ
time-dependent interaction Hamiltonian ⓘ |
| componentOf | standard formalism of perturbative quantum field theory ⓘ |
| describes | perturbative expansion of time-ordered exponentials ⓘ |
| field |
quantum field theory
ⓘ
theoretical physics ⓘ |
| generalizes | exponential of a time-dependent operator with non-commuting values ⓘ |
| historicalContext | introduced in the mid-20th century ⓘ |
| implies | series expansion in powers of the coupling constant ⓘ |
| involves |
interaction Hamiltonian density
ⓘ
time-ordered integrals over interaction times ⓘ time-ordering operator ⓘ |
| mathematicalForm | time-ordered exponential expressed as a time-ordered series of integrals ⓘ |
| namedAfter | Freeman Dyson ⓘ |
| provides | basis of the Dyson series ⓘ |
| relatesTo |
Feynman diagrams
ⓘ
S-matrix expansion ⓘ interaction picture ⓘ perturbation theory in quantum field theory ⓘ time-evolution operator ⓘ time-ordered products of operators ⓘ |
| usedBy |
particle physicists
ⓘ
quantum field theorists ⓘ |
| usedFor |
computing interaction effects in quantum field theory
ⓘ
expanding time-evolution operator in the interaction picture ⓘ |
| usedIn |
construction of Dyson series
ⓘ
covariant perturbation theory ⓘ derivation of perturbative S-matrix elements ⓘ |
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: Dyson’s formula Description of subject: Dyson’s formula is a key expression in quantum field theory that provides the perturbative expansion of time-ordered exponentials, forming the basis of the Dyson series used to compute interaction effects.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.