Jerzy Lewandowski

Bio: Jerzy Lewandowski is an academic researcher from University of Warsaw. The author has contributed to research in topics: Quantum gravity & Loop quantum gravity. The author has an hindex of 46, co-authored 201 publications receiving 13291 citations. Previous affiliations of Jerzy Lewandowski include University of Florida & Syracuse University.

Quantum group connections

Abstract: The Ahtekar-Isham C*-algebra known from Loop Quantum Gravity is the algebra of continuous functions on the space of (generalized) connections with a compact structure Lie group. The algebra can be constructed by some inductive techniques from the C*-algebra of continuous functions on the group and a family of graphs embedded in the manifold underlying the connections. We generalize the latter construction replacing the commutative C*-algebra of continuous functions on the group by a non-commutative C*-algebra defining a compact quantum group.

Relation between polymer and Fock excitations

Abstract: To bridge the gap between background independent, non-perturbative quantum gravity and low energy physics described by perturbative field theory in Minkowski space-time, Minkowskian Fock states are located, analyzed and used in the background independent framework. This approach to the analysis of semi-classical issues is motivated by recent results of Varadarajan. As in that work, we use the simpler U(1) example to illustrate our constructions but, in contrast to that work, formulate the theory in such a way that it can be extended to full general relativity.

Operator Spin Foam Models

Abstract: The goal of this paper is to introduce a systematic approach to spin foams. We define operator spin foams, that is foams labelled by group representations and operators, as the main tool. An equivalence relation we impose in the set of the operator spin foams allows to split the faces and the edges of the foams. The consistency with that relation requires introduction of the (familiar for the BF theory) face amplitude. The operator spin foam models are defined quite generally. Imposing a maximal symmetry leads to a family we call natural operator spin foam models. This symmetry, combined with demanding consistency with splitting the edges, determines a complete characterization of a general natural model. It can be obtained by applying arbitrary (quantum) constraints on an arbitrary BF spin foam model. In particular, imposing suitable constraints on Spin(4) BF spin foam model is exactly the way we tend to view 4d quantum gravity, starting with the BC model and continuing with the EPRL or FK models. That makes our framework directly applicable to those models. Specifically, our operator spin foam framework can be translated into the language of spin foams and partition functions. We discuss the examples: BF spin foam model, the BC model, and the model obtained by application of our framework to the EPRL intertwiners.

Observer’s observables. Residual diffeomorphisms

Abstract: We investigate the fate of diffeomorphisms when the radial gauge is imposed in canonical general relativity. As shown elsewhere, the radial gauge is closely related to the observer's observables. These observables are invariant under a large subgroup of diffeomorphisms which results in their usefulness for canonical general relativity. There are, however, some diffeomorphisms, called residual diffeomorphisms, which might be 'observed' by the observer as they do not preserve her observables. The present paper is devoted to the analysis of these diffeomorphisms in the case of the spatial and spacetime radial gauges. Although the residual diffeomorphisms do not form a subgroup of all diffeomorphisms, we show that their induced action in the phase space does form a group. We find the generators of the induced transformations and compute the structure functions of the algebras they form. The obtained algebras are deformations of the algebra of the Euclidean group and the algebra of the Poincare group in the spatial and spacetime case, respectively. In both cases the deformation depends only on the Riemann curvature tensor and in particular vanishes when the space or spacetime is flat.

Extremal horizons stationary to the second order: New constraints

Abstract: We consider nonexpanding shear-free (NE-SF) null surface geometries embeddable as extremal Killing horizons to the second order in Einstein vacuum spacetimes. A NE-SF null surface geometry consists of a degenerate metric tensor and a consistent torsion free covariant derivative. We derive the constraints implied by the existence of an embedding. The first constraint is well known as the near-horizon geometry equation. The second constraint we find is new. The constraints lead to a complete characterization of those NE-SF null geometries that are embeddable in the extremal Kerr spacetime. Our results are also valid for spacetimes with a cosmological constant.

Background independent quantum gravity: A Status report

Abstract: The goal of this review is to present an introduction to loop quantum gravity—a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation is pedagogical. Thus, in addition to providing a bird's eye view of the present status of the subject, the review should also serve as a vehicle to enter the field and explore it in detail. To aid non-experts, very little is assumed beyond elements of general relativity, gauge theories and quantum field theory. While the review is essentially self-contained, the emphasis is on communicating the underlying ideas and the significance of results rather than on presenting systematic derivations and detailed proofs. (These can be found in the listed references.) The subject can be approached in different ways. We have chosen one which is deeply rooted in well-established physics and also has sufficient mathematical precision to ensure that there are no hidden infinities. In order to keep the review to a reasonable size, and to avoid overwhelming non-experts, we have had to leave out several interesting topics, results and viewpoints; this is meant to be an introduction to the subject rather than an exhaustive review of it.

Quantum Nature of the Big Bang: Improved dynamics

Abstract: An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The scalar field continues to serve as ''emergent time'', the big bang is again replaced by a quantum bounce, and quantum evolution remains deterministic across the deep Planck regime. However, while with the Hamiltonian constraint used so far in loop quantum cosmology the quantum bounce can occur even at low matter densities, with the new Hamiltonian constraint it occurs only at a Planck-scale density. Thus, the new quantum dynamics retains the attractive features of current evolutions in loop quantum cosmology but, at the same time, cures their main weakness.

Loop Quantum Cosmology: A Status Report

Abstract: Loop quantum cosmology (LQC) is the result of applying principles of loop quantum gravity (LQG) to cosmological settings. The distinguishing feature of LQC is the prominent role played by the quantum geometry effects of LQG. In particular, quantum geometry creates a brand new repulsive force which is totally negligible at low spacetime curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction. In cosmological models, while Einstein's equations hold to an excellent degree of approximation at low curvature, they undergo major modifications in the Planck regime: for matter satisfying the usual energy conditions, any time a curvature invariant grows to the Planck scale, quantum geometry effects dilute it, thereby resolving singularities of general relativity. Quantum geometry corrections become more sophisticated as the models become richer. In particular, in anisotropic models, there are significant changes in the dynamics of shear potentials which tame their singular behavior in striking contrast to older results on anisotropies in bouncing models. Once singularities are resolved, the conceptual paradigm of cosmology changes and one has to revisit many of the standard issues—e.g. the 'horizon problem'—from a new perspective. Such conceptual issues as well as potential observational consequences of the new Planck scale physics are being explored, especially within the inflationary paradigm. These considerations have given rise to a burst of activity in LQC in recent years, with contributions from quantum gravity experts, mathematical physicists and cosmologists. The goal of this review is to provide an overview of the current state of the art in LQC for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general and cosmologists who wish to apply LQC to probe modifications in the standard paradigm of the early universe. In this review, effort has been made to streamline the material so that each of these communities can read only the sections they are most interested in, without loss of continuity.