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gravity

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Context

Gravity

gravity, supergravity

Formalism

Definition

Spacetime configurations

Properties

Models

Quantum theory

Physics

physics

Contents

Idea

Gravity is a gauge theory over the Poincare group.

The gravitational field on a spacetime X is a connection that is locally a Lie algebra-valued 1-form with values in the Poincare Lie algebra.

(E,Ω):TX→𝔦𝔰𝔬(d−1,1).(E, \Omega) : T X \to \mathfrak{iso}(d-1,1) \,.

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

The non-propagating field? Ω 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 X 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):TX→𝔰𝔦𝔰𝔬(d−1,1)(E,\Omega, \Psi) : T X \to \mathfrak{siso}(d-1,1)

The additional fermionic field Ψ is the gravitino field.

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

Details

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

References

General

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 October 12, 2011 16:07:44 by Urs Schreiber (131.211.234.95)
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