A field configuration of the physical theory of gravity on a spacetime is equivalently
(This parameterization of the gravitational field is called the first-order formulation of gravity.) The component of the connection is the vielbein that encodes a pseudo-Riemannian metric on and makes a pseudo-Riemannian manifold. Its quanta are the gravitons.
The non-propagating field? 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 for the super Poincare group. The field of supergravity is a Lie-algebra valued form with values in the super Poincare Lie algebra.
The additional fermionic field is the gravitino field.
So the configuration space of gravity on some is essentially the moduli space of Riemannian metrics on .
for the moment see D'Auria-Fre formulation of supergravity for further details
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)
Revised on January 6, 2013 20:12:42
by Urs Schreiber