nLab
gravity

Context

Gravity

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

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.

Details

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

References

General

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

Non-renormalizability

The result that gravity is not renormalizable is due to

Review includes

Revised on June 27, 2017 09:26:20 by Urs Schreiber (131.220.184.222)