nLab gravity





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Surveys, textbooks and lecture notes

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A field configuration of the physical theory of gravity on a spacetime XX is equivalently

(This parameterization of the gravitational field is called the first-order formulation of gravity.) The component EE of the connection is the vielbein that encodes a pseudo-Riemannian metric g=EEg = E \cdot E on XX and makes XX a pseudo-Riemannian manifold. Its quanta are the gravitons.

The “non-propagating field” Ω\Omega is the spin connection.

The action functional on the space of such connection which defines the classical field theory of gravity is the Einstein-Hilbert action.

More generally, supergravity is a gauge theory over a supermanifold XX for the super Poincare group. The field of supergravity is a Lie-algebra valued form with values in the super Poincare Lie algebra.

(E,Ω,Ψ):TX𝔰𝔦𝔰𝔬(d1,1) (E,\Omega, \Psi) : T X \to \mathfrak{siso}(d-1,1)

The additional fermionic field Ψ\Psi is the gravitino field.

So the configuration space of gravity on some XX is essentially the moduli space of Riemannian metrics on XX.


for the moment see D'Auria-Fre formulation of supergravity for further details



Historical texts:

  • Leopold Infeld (ed.), Relativistic Theories of Gravitation, Proceedings of a conference held in Warsaw and Jablonna 1962, Pergamon Press (1964) [pdf]

Textbook accounts:

Background on pseudo-?Riemannian geometry:

Lecture notes:

See also

On gravity in relation to thermodynamics:

Discussion of classical gravity via its perturbative quantum field theory:

This way the theory of gravity based on the standard Einstein-Hilbert action may be regarded as just an effective quantum field theory, which makes some of its notorious problems be non-problems:

Relation of the first-order formulation of gravity to BF-theory:

See also the references at general relativity.

Covariant phase space

The (reduced) covariant phase space of gravity (presented for instance by its BV-BRST complex, see there fore more details) is discussed for instance in

which is surveyed in

  • Katarzyna Rejzner, The BV formalism applied to classical gravity (pdf)

Careful discussion of observables in gravity is in

Further discussion of the phase space of gravity in first-order formulation via BV-BFV formalism:

Discussion of flux-observables:


The result that gravity is not renormalizable is due to:


Last revised on June 23, 2024 at 12:35:14. See the history of this page for a list of all contributions to it.