Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userInducing Barbero-Immirzi Connections along SU(2)-reductions of Bundles on Spacetime
113
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We shall present here a general apt technique to induce connections along bundle reductions which is different from the standard restriction. This clarifies and generalizes the standard procedure to define Barbero-Immirzi (BI) connection, though on spacetime. The standard spacial BI connection used in LQG is then obtained by its spacetime version by standard restriction. The general prescription to define such a reduced connection is interesting from a mathematical viewpoint and it allows a general and direct control on transformation laws of the induced object. Moreover, unlike what happens by using standard restriction, we shall show that once a bundle reduction is given, then any connection induces a reduced connection with no constraint on the original holonomy as it happens when connections are simply restricted.
rate research
Read More
We propose an approach to induced gravity, or Sakharovs metrical elasticity, which requires only an affine spacetime that accommodates scalar fields. The setup provides the induction of metric gravity from a pure affine action, and it is established in two possible ways: (i) at the classical level, Einstein-Hilbert action arises with both, metric and Newtons constant, from the nonzero potential energy of the background field (ii) at the quantum level (quantized matter), gravity scale is induced from the one-loop effective action by integrating out the scalar degrees of freedom. In the former, the cosmological constant is absorbed leading to the gravitational sector, however, the fact remains that quantum corrections induce a large cosmological constant. This new approach adds a crucial feature to induced gravity which is the fact that the metric structure is not imposed from the scratch, but it is an outcome of the primary theory.
For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action of the Lie 2-group and a pullback operation along Morita equivalences between Lie groupoids. Using this notion, we define connections on principal 2-bundles as Lie 2-algebra-valued 1-forms on the total space Lie groupoid of the 2-bundle, satisfying a condition in complete analogy to connections on ordinary principal bundles. We carefully treat various notions of curvature, and prove a classification result by the non-abelian differential cohomology of Breen-Messing. This provides a consistent, global perspective to higher gauge theory.
We propose a novel BF-type formulation of real four-dimensional gravity, which generalizes previous models. In particular, it allows for an arbitrary Immirzi parameter. We also construct the analogue of the Urbantke metric for this model.
We define and study natural $mathrm{SU}(2)$-structures, in the sense of Conti-Salamon, on the total space $cal S$ of the tangent sphere bundle of any given oriented Riemannian 3-manifold $M$. We recur to a fundamental exterior differential system of Riemannian geometry. Essentially, two types of structures arise: the contact-hypo and the non-contact and, for each, we study the conditions for being hypo, nearly-hypo or double-hypo. We discover new double-hypo structures on $S^3times S^2$, of which the well-known Sasaki-Einstein are a particular case. Hyperbolic geometry examples also appear. In the search of the associated metrics, we find a theorem, useful for explicitly determining the metric, which applies to all $mathrm{SU}(2)$-structures in general. Within our application to tangent sphere bundles, we discover a whole new class of metrics specific to 3d-geometry. The evolution equations of Conti-Salamon are considered; leading to a new integrable $mathrm{SU}(3)$-structure on ${cal S}timesmathbb{R}_+$ associated to any flat $M$.
We state and prove a simple Theorem that allows one to generate invariant quantities in Metric-Affine Geometry, under a given transformation of the affine connection. We start by a general functional of the metric and the connection and consider transformations of the affine connection possessing a certain symmetry. We show that the initial functional is invariant under the aforementioned group of transformations iff its $Gamma$-variation produces tensor of a given symmetry. Conversely if the tensor produced by the $Gamma$-variation of the functional respects a certain symmetry then the functional is invariant under the associated transformation of the affine connection. We then apply our results in Metric-Affine Gravity and produce invariant actions under certain transformations of the affine connection. Finally, we derive the constraints put on the hypermomentum for such invariant Theories.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
