Bogoliubov transformation
E461415
The Bogoliubov transformation is a mathematical change of basis used in quantum field theory and many-body physics to diagonalize Hamiltonians by mixing creation and annihilation operators, enabling the description of quasiparticles and phenomena like superconductivity.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Bogoliubov transformation canonical | 3 |
| Bogoliubov quasiparticles | 1 |
| Bogoliubov transformations | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4681193 — 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: Bogoliubov transformation Context triple: [Nikolay Bogolyubov, notableWork, Bogoliubov transformation]
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A.
Jordan–Wigner transformation
The Jordan–Wigner transformation is a mathematical mapping in quantum many-body physics that converts spin operators into fermionic creation and annihilation operators, enabling the study of spin systems using fermionic methods.
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B.
Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
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C.
Infeld–van der Waerden formalism
The Infeld–van der Waerden formalism is a mathematical framework in general relativity that reformulates the theory using spinor calculus to describe gravitational and electromagnetic fields.
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D.
Onsager algebra
The Onsager algebra is an infinite-dimensional Lie algebra introduced in the study of exactly solvable models in statistical mechanics, particularly the two-dimensional Ising model.
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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: Bogoliubov transformation Target entity description: The Bogoliubov transformation is a mathematical change of basis used in quantum field theory and many-body physics to diagonalize Hamiltonians by mixing creation and annihilation operators, enabling the description of quasiparticles and phenomena like superconductivity.
-
A.
Jordan–Wigner transformation
The Jordan–Wigner transformation is a mathematical mapping in quantum many-body physics that converts spin operators into fermionic creation and annihilation operators, enabling the study of spin systems using fermionic methods.
-
B.
Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
-
C.
Infeld–van der Waerden formalism
The Infeld–van der Waerden formalism is a mathematical framework in general relativity that reformulates the theory using spinor calculus to describe gravitational and electromagnetic fields.
-
D.
Onsager algebra
The Onsager algebra is an infinite-dimensional Lie algebra introduced in the study of exactly solvable models in statistical mechanics, particularly the two-dimensional Ising model.
-
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 (48)
| Predicate | Object |
|---|---|
| instanceOf |
canonical transformation
ⓘ
change of basis ⓘ linear transformation ⓘ mathematical transformation ⓘ |
| appliesTo |
bosonic operators
ⓘ
fermionic operators ⓘ |
| expresses | new quasiparticle operators as linear combinations of old operators ⓘ |
| field |
condensed matter physics
ⓘ
many-body physics ⓘ quantum field theory ⓘ statistical mechanics ⓘ |
| goal | to obtain a Hamiltonian that is diagonal in quasiparticle operators ⓘ |
| hasProperty |
canonical
ⓘ
invertible ⓘ linear in creation and annihilation operators ⓘ symplectic in bosonic case ⓘ unitary in fermionic case ⓘ |
| involves | coherence factors u and v ⓘ |
| mathematicallyFormulatedAs | linear transformation between two sets of ladder operators ⓘ |
| namedAfter | Nikolay Bogoliubov NERFINISHED ⓘ |
| preserves |
canonical anticommutation relations
ⓘ
canonical commutation relations ⓘ |
| relatedTo |
BCS ground state
NERFINISHED
ⓘ
Bogoliubov quasiparticles NERFINISHED ⓘ Bogoliubov–de Gennes equations NERFINISHED ⓘ Hartree–Fock–Bogoliubov theory NERFINISHED ⓘ Nambu spinor formalism ⓘ quasiparticle operators ⓘ |
| usedFor |
defining quasiparticles
ⓘ
describing superconductivity ⓘ describing superfluidity ⓘ diagonalizing Hamiltonians ⓘ diagonalizing quadratic Hamiltonians ⓘ mixing creation and annihilation operators ⓘ quantizing fields with pairing terms ⓘ removing anomalous terms in Hamiltonians ⓘ solving BCS theory of superconductivity ⓘ treating interacting Bose gases ⓘ treating interacting Fermi systems ⓘ |
| usedIn |
BCS theory of superconductivity
NERFINISHED
ⓘ
Bogoliubov theory of weakly interacting Bose gas NERFINISHED ⓘ Hawking radiation calculations ⓘ Unruh effect analysis ⓘ mean-field approximations ⓘ particle creation in curved spacetime ⓘ quantum optics ⓘ squeezed state formalism ⓘ theory of superfluid helium ⓘ |
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: Bogoliubov transformation Description of subject: The Bogoliubov transformation is a mathematical change of basis used in quantum field theory and many-body physics to diagonalize Hamiltonians by mixing creation and annihilation operators, enabling the description of quasiparticles and phenomena like superconductivity.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Bogoliubov transformations
this entity surface form:
Bogoliubov quasiparticles