TY - JOUR

T1 - Gravity and the Poincare group

AU - Nardelli, Giuseppe

AU - Grignani, Gianluca

AU - Grignani, G.

AU - Nardelli, G.

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

KW - Gravity

KW - gauge theory of gravity

KW - Gravity

KW - gauge theory of gravity

UR - http://hdl.handle.net/10807/8568

UR - http://prd.aps.org/abstract/prd/v45/i8/p2719_1

U2 - 10.1103/PhysRevD.45.2719

DO - 10.1103/PhysRevD.45.2719

M3 - Article

VL - 1991

SP - 2719

EP - 2731

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

ER -