Faddeev–Popov ghosts

E860357

Grassmann-valued field anticommuting field auxiliary field concept in quantum field theory ghost field tool in path integral quantization

Faddeev–Popov ghosts are auxiliary, anticommuting fields introduced in the path integral quantization of non-Abelian gauge theories to correctly account for gauge redundancy and maintain unitarity and renormalizability.

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All labels observed (9)

Label	Occurrences
BRST symmetry	2
Faddeev–Popov ghosts canonical	2
BRST formalism	1
BRST-like symmetry	1
Faddeev and Popov 1967 paper on gauge fields	1
Faddeev–Popov determinant	1
Faddeev–Popov procedure	1
Faddeev–Popov quantization	1
Fadeev–Popov method	1

How this entity was disambiguated

This entity first appeared as the object of triple T10376354 — 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: Faddeev–Popov ghosts
Context triple: [Yang–Mills theory, includesFeature, Faddeev–Popov ghosts]

A. Slavnov–Taylor identities
Slavnov–Taylor identities are relations in non-Abelian gauge theories that generalize Ward identities, ensuring the consistency and renormalizability of gauge-invariant quantum field theories.
B. Ward–Takahashi identities
The Ward–Takahashi identities are fundamental relations in quantum field theory that express the consequences of gauge or global symmetries for Green’s functions and ensure the consistency of renormalization with these symmetries.
C. Schwinger–Dyson equations
The Schwinger–Dyson equations are a set of integral equations in quantum field theory that relate correlation functions and encode the full dynamics of a quantum field.
D. Faddeev’s axioms
Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
E. Polyakov loop
The Polyakov loop is a gauge-invariant observable in finite-temperature quantum chromodynamics used to probe confinement and deconfinement phases of quarks and gluons.
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: Faddeev–Popov ghosts
Target entity description: Faddeev–Popov ghosts are auxiliary, anticommuting fields introduced in the path integral quantization of non-Abelian gauge theories to correctly account for gauge redundancy and maintain unitarity and renormalizability.

A. Slavnov–Taylor identities
Slavnov–Taylor identities are relations in non-Abelian gauge theories that generalize Ward identities, ensuring the consistency and renormalizability of gauge-invariant quantum field theories.
B. Ward–Takahashi identities
The Ward–Takahashi identities are fundamental relations in quantum field theory that express the consequences of gauge or global symmetries for Green’s functions and ensure the consistency of renormalization with these symmetries.
C. Schwinger–Dyson equations
The Schwinger–Dyson equations are a set of integral equations in quantum field theory that relate correlation functions and encode the full dynamics of a quantum field.
D. Faddeev’s axioms
Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
E. Polyakov loop
The Polyakov loop is a gauge-invariant observable in finite-temperature quantum chromodynamics used to probe confinement and deconfinement phases of quarks and gluons.
F. None of above. chosen

Statements (49)

Predicate	Object
instanceOf	Grassmann-valued field ⓘ anticommuting field ⓘ auxiliary field ⓘ concept in quantum field theory ⓘ ghost field ⓘ tool in path integral quantization ⓘ
anticommutationProperty	Grassmann-odd ⓘ
appearIn	BRST-invariant Lagrangian ⓘ Faddeev–Popov procedure ⓘ linked to: Faddeev–Popov ghosts gauge-fixed action ⓘ
appearInGauge	Feynman gauge ⓘ Landau gauge ⓘ Rξ gauges ⓘ
associatedWith	gauge group generators ⓘ
contributeTo	loop corrections ⓘ
doNotAppearAs	asymptotic physical states ⓘ external lines in physical S-matrix elements ⓘ
enterAs	additional fields in the gauge-fixed Lagrangian ⓘ
fieldType	complex scalar Grassmann field ⓘ
introducedBy	Ludvig Faddeev ⓘ linked to: Ludwig Faddeev Victor Popov NERFINISHED ⓘ
introducedIn	path integral formalism ⓘ
introducedInPublication	Faddeev and Popov 1967 paper on gauge fields ⓘ linked to: Faddeev–Popov ghosts
introducedTo	correctly account for gauge volume factor ⓘ ensure renormalizability ⓘ fix gauge in path integrals ⓘ handle gauge redundancy ⓘ maintain unitarity ⓘ
liveIn	adjoint representation of the gauge group ⓘ
LorentzTransformationProperty	scalar ⓘ
mathematicalRole	represent Faddeev–Popov determinant ⓘ
namedAfter	Ludvig Faddeev ⓘ linked to: Ludwig Faddeev Victor Popov NERFINISHED ⓘ
notRequiredIn	Abelian gauge theories in simple gauges ⓘ
propagateIn	internal lines of Feynman diagrams ⓘ
relatedConcept	BRST symmetry ⓘ Faddeev–Popov determinant ⓘ linked to: Faddeev–Popov ghosts Fadeev–Popov method ⓘ linked to: Faddeev–Popov ghosts Slavnov–Taylor identities ⓘ gauge fixing ⓘ
requiredIn	covariant gauge quantization of non-Abelian theories ⓘ
roleInGaugeTheories	cancel unphysical gauge degrees of freedom ⓘ ensure consistency of quantization of non-Abelian fields ⓘ preserve gauge invariance at quantum level ⓘ
spin	0 ⓘ
statistics	fermionic ⓘ
usedIn	Yang–Mills theory ⓘ non-Abelian gauge theory ⓘ quantum chromodynamics ⓘ

How these facts were elicited

Referenced by (11)

Full triples — surface form annotated when it differs from this entity's canonical label.

Yang–Mills theory → includesFeature → Faddeev–Popov ghosts ⓘ

't Hooft–Veltman gauge → relatedTo → Faddeev–Popov ghosts ⓘ

subject linked to: ’t Hooft–Veltman gauge

't Hooft–Veltman gauge → relatedTo → BRST symmetry ⓘ

subject linked to: ’t Hooft–Veltman gauge