Hamiltonian (time translation generator)
E166696
generator in Poincaré algebra
generator of time translations
observable in quantum mechanics
operator in quantum theory
The Hamiltonian (time translation generator) is the operator in relativistic quantum theory that generates time evolution of physical states as part of the Poincaré symmetry algebra.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Hamiltonian function | 3 |
| Hamiltonian (time translation generator) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1463242 — 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: Hamiltonian (time translation generator) Context triple: [Poincaré group, hasGenerator, Hamiltonian (time translation generator)]
-
A.
Noether's theorem
Noether's theorem is a fundamental result in theoretical physics and mathematics that links continuous symmetries of a physical system to corresponding conservation laws, such as energy or momentum conservation.
-
B.
Poincaré group
The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
-
C.
Noether charge
A Noether charge is a conserved quantity associated with a continuous symmetry of a physical system, arising from Noether's theorem.
-
D.
Peierls bracket
The Peierls bracket is a covariant generalization of the Poisson bracket used in quantum field theory and classical field theory to define commutation relations in a way that respects spacetime causality.
-
E.
Wheeler–DeWitt equation
The Wheeler–DeWitt equation is a fundamental equation in quantum gravity that attempts to describe the quantum state of the entire universe without reference to time.
- 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: Hamiltonian (time translation generator) Target entity description: The Hamiltonian (time translation generator) is the operator in relativistic quantum theory that generates time evolution of physical states as part of the Poincaré symmetry algebra.
-
A.
Noether's theorem
Noether's theorem is a fundamental result in theoretical physics and mathematics that links continuous symmetries of a physical system to corresponding conservation laws, such as energy or momentum conservation.
-
B.
Poincaré group
The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
-
C.
Noether charge
A Noether charge is a conserved quantity associated with a continuous symmetry of a physical system, arising from Noether's theorem.
-
D.
Peierls bracket
The Peierls bracket is a covariant generalization of the Poisson bracket used in quantum field theory and classical field theory to define commutation relations in a way that respects spacetime causality.
-
E.
Wheeler–DeWitt equation
The Wheeler–DeWitt equation is a fundamental equation in quantum gravity that attempts to describe the quantum state of the entire universe without reference to time.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
generator in Poincaré algebra
ⓘ
generator of time translations ⓘ observable in quantum mechanics ⓘ operator in quantum theory ⓘ |
| actsOn | Hilbert space of physical states ⓘ |
| appearsIn |
Heisenberg operator formulation of quantum mechanics
ⓘ
surface form:
Heisenberg picture
Schrödinger picture ⓘ |
| belongsTo |
Poincaré group
ⓘ
surface form:
Poincaré symmetry algebra
|
| commutesWith | spatial momentum operators in time-independent systems ⓘ |
| correspondsTo |
Poincaré group
ⓘ
surface form:
time translation subgroup of Poincaré group
|
| determines | spectrum of energy levels ⓘ |
| eigenvaluesRepresent | possible energy values ⓘ |
| generates | unitary time evolution operator ⓘ |
| generatesTransformation | |ψ(t)⟩ → e^{-iHt}|ψ(0)⟩ (ℏ=1) ⓘ |
| hasDimension | energy ⓘ |
| hasRole | generates time evolution of physical states ⓘ |
| implements | time translations on field operators in Heisenberg picture ⓘ |
| isAssociatedWith | Noether charge for time translation symmetry ⓘ |
| isBoundedBelow | true for stable relativistic theories ⓘ |
| isCentralTo | problem of time in quantum gravity ⓘ |
| isComponentOf | four-momentum operator ⓘ |
| isConjugateTo | time coordinate in canonical formalism ⓘ |
| isConservedWhen | Lagrangian is time-translation invariant ⓘ |
| isConstraintIn | generally covariant theories like canonical quantum gravity ⓘ |
| isDefinedOn | domain dense in Hilbert space ⓘ |
| isDenotedBy | H ⓘ |
| isFrameDependent | true in relativistic theories ⓘ |
| isGeneratorOf | one-parameter unitary group of time translations ⓘ |
| isHermitian | true ⓘ |
| isLinkedTo | stability and causality of relativistic theory ⓘ |
| isModifiedBy | interaction terms in interacting quantum field theories ⓘ |
| isObtainedFrom | Legendre transform of Lagrangian in canonical quantization ⓘ |
| isPartOf | ten generators of Poincaré symmetry ⓘ |
| isRelatedBy | H = P^0 in covariant notation ⓘ |
| isRelatedTo | energy of the system ⓘ |
| isSelfAdjoint | true ⓘ |
| isSubjectOf | spectral theorem for self-adjoint operators ⓘ |
| isUsedIn |
relativistic quantum field theory
ⓘ
relativistic quantum mechanics ⓘ |
| isUsedToDefine |
thermal (Gibbs) state via e^{-βH}
ⓘ
time-ordered correlation functions ⓘ |
| obeys |
[H,J^i]=0 in Poincaré algebra
ⓘ
[H,K^i]=iP^i in Poincaré algebra ⓘ [H,P^i]=0 for isolated relativistic systems ⓘ |
| reducesTo | classical Hamiltonian in ℏ → 0 limit ⓘ |
| satisfies |
H|0⟩ = 0 or E_0|0⟩ for vacuum state (up to constant)
ⓘ
Schrödinger equation ⓘ |
How these facts were elicited
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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: Hamiltonian (time translation generator) Description of subject: The Hamiltonian (time translation generator) is the operator in relativistic quantum theory that generates time evolution of physical states as part of the Poincaré symmetry algebra.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Hamiltonian function
this entity surface form:
Hamiltonian function
this entity surface form:
Hamiltonian function