We discuss gravity as a gauge theory of the Poincaré group in three and four dimensions, i.e., in a metric-independent fashion. The fundamental fields of the theory are the gauge potentials, the matter fields, and the so-called Poincaré coordinates qa(x) a set of fields that are defined on the space-time manifold, but that transform as Poincaré vectors under gauge transformations. The presence of such coordinates is necessary in order to construct a gauge theory of the Poincaré group. We discuss the procedure needed to connect this theory with the Einsteinian formulation of gravity, and we show that the field equations for the gauge potentials, for pointlike sources, and for scalar and spinor matter fields reproduce the Einstein equations, the geodesics equations, and the Klein-Gordon and the Dirac equations in curved space-time, respectively. In 2+1 dimensions and in the presence of pointlike sources this gauge-theoretical approach can be further developed: the gauge potentials can be written almost everywhere as pure gauge, and a solution of the field equations provides, at the same time, the space-time metric and the set of coordinates that globally flatten the metric.

Nardelli, G., Grignani, G., Gravity and the Poincare group, <<PHYSICAL REVIEW D>>, 1991; 1991 (D45): 2719-2731. [doi:10.1103/PhysRevD.45.2719] [http://hdl.handle.net/10807/8568]

Gravity and the Poincare group

Nardelli, Giuseppe;Grignani, Gianluca
1991

Abstract

We discuss gravity as a gauge theory of the Poincaré group in three and four dimensions, i.e., in a metric-independent fashion. The fundamental fields of the theory are the gauge potentials, the matter fields, and the so-called Poincaré coordinates qa(x) a set of fields that are defined on the space-time manifold, but that transform as Poincaré vectors under gauge transformations. The presence of such coordinates is necessary in order to construct a gauge theory of the Poincaré group. We discuss the procedure needed to connect this theory with the Einsteinian formulation of gravity, and we show that the field equations for the gauge potentials, for pointlike sources, and for scalar and spinor matter fields reproduce the Einstein equations, the geodesics equations, and the Klein-Gordon and the Dirac equations in curved space-time, respectively. In 2+1 dimensions and in the presence of pointlike sources this gauge-theoretical approach can be further developed: the gauge potentials can be written almost everywhere as pure gauge, and a solution of the field equations provides, at the same time, the space-time metric and the set of coordinates that globally flatten the metric.
1991
Inglese
Nardelli, G., Grignani, G., Gravity and the Poincare group, <<PHYSICAL REVIEW D>>, 1991; 1991 (D45): 2719-2731. [doi:10.1103/PhysRevD.45.2719] [http://hdl.handle.net/10807/8568]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/8568
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 91
  • ???jsp.display-item.citation.isi??? 84
social impact