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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



Textbooks include

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:

  • John F. Donoghue, Introduction to the Effective Field Theory Description of Gravity (arXiv:gr-qc/9512024)

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


The result that gravity is not renormalizable is due to

Review includes

Revised on June 22, 2017 07:19:57 by Urs Schreiber (