Plebański action for gravity

E811627

first-order formulation of gravity gravitational action principle reformulation of general relativity self-dual formulation of gravity

The Plebański action for gravity is a reformulation of general relativity that expresses the gravitational field in terms of self-dual two-forms and connections, forming the basis for several modern approaches to quantum gravity.

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Statements (49)

Predicate	Object
instanceOf	first-order formulation of gravity ⓘ gravitational action principle ⓘ reformulation of general relativity ⓘ self-dual formulation of gravity ⓘ
aimsTo	provide a background-independent starting point for quantization ⓘ simplify the canonical formulation of general relativity ⓘ
appliesTo	Lorentzian signature metrics ⓘ Riemannian signature metrics ⓘ
coreIdea	fundamental variables are two-forms and connections instead of the metric ⓘ gravity as a constrained BF theory ⓘ imposition of simplicity constraints recovers general relativity ⓘ
describes	Einstein’s theory of gravity ⓘ
equivalentTo	Einstein–Hilbert action (on shell) NERFINISHED ⓘ Palatini action (on shell) NERFINISHED ⓘ tetrad formulation of general relativity (on shell) ⓘ
field	classical general relativity ⓘ quantum gravity ⓘ theoretical physics ⓘ
formulatedIn	four spacetime dimensions ⓘ
generalizationOf	pure BF theory with constraints ⓘ
hasVariant	Holst-modified Plebański action NERFINISHED ⓘ Plebański action with cosmological constant NERFINISHED ⓘ chiral (self-dual) Plebański action NERFINISHED ⓘ non-chiral Plebański action NERFINISHED ⓘ
historicalContext	developed in the 1970s ⓘ
includesTerm	cosmological constant term in some formulations ⓘ
inspired	constrained BF approaches to quantum gravity ⓘ spin foam quantization of gravity ⓘ
involves	Lagrange multipliers enforcing constraints ⓘ complex variables in Lorentzian signature ⓘ self-dual part of the curvature ⓘ
mathematicalStructure	gauge-theoretic formulation of gravity ⓘ uses differential forms and exterior calculus ⓘ
namedAfter	Jerzy Plebański NERFINISHED ⓘ
relatedTo	Ashtekar variables NERFINISHED ⓘ Barrett–Crane model NERFINISHED ⓘ EPRL–FK spin foam models NERFINISHED ⓘ loop quantum gravity NERFINISHED ⓘ self-dual Ashtekar connection NERFINISHED ⓘ spin foam models ⓘ
usedIn	covariant approaches to quantum gravity ⓘ path-integral formulations of gravity ⓘ
usesConcept	BF theory NERFINISHED ⓘ SU(2) connection ⓘ connection one-forms ⓘ self-dual part of the spin connection ⓘ self-dual two-forms ⓘ simplicity constraints ⓘ tetrad formalism ⓘ

Referenced by (1)

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

Jerzy Plebański → hasConcept → Plebański action for gravity ⓘ