Gravity and the Poincaré group

Vacuum correlations at geodesic distance in quantum gravity

“…A consistent gauge formulation can be obtained only introducing some auxiliary fields q a [Grignani and Nardelli, 1992]. …”

Non-perturbative particle dynamics in (2+1)-gravity

“…However, the localized curvature due to particles' momenta implies that the Minkowskian coordinates are not single-valued, but are changed by a Poincare' transformation by parallel transport around the sources ( DJH matching conditions [2] ). This implies that the metric description requires singularity tails carried by each particle [9]- [10].…”

“…The latter hold in the region outside the singularity tails departing from each particle source, which are needed in order to define a Riemann surface for the X's , and carry a non-trivial, localized spin connection, discussed elsewhere [9]- [10].…”

R+S2 theories of gravity without big-bang singularity

“…[9] is used, L G is the gravitational Lagrangian, R is the scalar curvature, Λ is the positive cosmological constant, S cab = g cd S d ab , S d ab is the torsion tensor, g cd is the metric tensor, S a = S c ac , a, b, c, etc., are abstract indices [21,22], and a 1 , a 2 , a 3 are three dimensionless parameters. The Lagrangian (1) is gauge invariant because each of the metric, torsion and curvature can be expressed in a gauge-invariant way [2][3][4][8][9][10]. Moreover, the Lagrangian is complete in the sense that it contains all components of the gravitational field strength F ab , i.e., it contains both curvature and torsion.…”

“…The spacetime torsion is introduced in the gauge theory of gravity [1][2][3][4][5][6][7][8][9][10] to realize the local Poincaré, de Sitter (dS) or Anti-de Sitter (AdS) symmetry. It is shown that the torsion effect in the Einstein-Cartan (EC) theory, which is the simplest model of the gauge theory of gravity, may avert the initial singularity of the homogeneous but anisotropic universe [11], where the matter fields are described by a spin fluid [12].…”