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.

Hamiltonian operator for loop quantum gravity coupled to a scalar field

Abstract: We present the construction of a physical Hamiltonian operator in the deparametrized model of loop quantum gravity coupled to a free scalar field. This construction is based on the use of the recently introduced curvature operator, and on the idea of so-called "special loops". We discuss in detail the regularization procedure and the assignment of the loops, along with the properties of the resulting operator. We compute the action of the squared Hamiltonian operator on spin network states, and close with some comments and outlooks.

Mechanics of multidimensional isolated horizons

Abstract: Recently, a multidimensional generalization of the isolated horizon framework has been proposed (Lewandowski and Pawlowski 2005 Class. Quantum Grav. 22 1573–98). Therein the geometric description was easily generalized to higher dimensions and the structure of the constraints induced by the Einstein equations was analysed. In particular, the geometric version of the zeroth law of black-hole thermodynamics was proved. In this work, we show how the IH mechanics can be formulated in a dimension-independent fashion and derive the first law of BH thermodynamics for arbitrarily dimensional IH. We also propose a definition of energy for non-rotating horizons.

Physical time and other conceptual issues of quantum gravity on the example of loop quantum cosmology

Abstract: Several conceptual aspects of quantum gravity (QG) are studied on the example of the homogeneous isotropic loop quantum cosmology (LQC) model. In particular: (i) the proper time of the comoving observers is shown to be a quantum operator and a quantum spacetime metric tensor operator is derived. (ii) Solutions of the quantum scalar constraint for two different choices of the lapse function are compared and contrasted. In particular it is shown that in the case of a model with massless scalar field and cosmological constant Λ, the physical Hilbert spaces constructed for two choices of lapse are the same for Λ 0. (iii) The mechanism of the singularity avoidance is analyzed via detailed studies of an energy density operator, whose essential spectrum was shown to be an interval , where . (iv) The relation between the kinematical and the physical quantum geometry is discussed on the level of relation between observables.

Group of loops, holonomy maps, path bundle and path connection

Abstract: Several new results are established concerning the theory of connections in the context of holonomy maps and the group of loops in a given manifold. In particular the Kernel theorem is formulated and proved; it leads to the reconstruction of a connection and a bundle directly from the loops which set up the kernel of a holonomy map.

Spacetimes foliated by Killing horizons

Abstract: It seems to be expected that a horizon of a quasi-local type, such as a Killing or an isolated horizon, by analogy with a globally defined event horizon, should be unique in some open neighbourhood in the spacetime, provided the vacuum Einstein or the Einstein–Maxwell equations are satisfied. The aim of our paper is to verify whether that intuition is correct. If one can extend a so-called Kundt metric, in such a way that its null, shear-free surfaces have spherical spacetime sections, the resulting spacetime is foliated by socalled non-expanding horizons. The obstacle is Kundt’s constraint induced at the surfaces by the Einstein or the Einstein–Maxwell equations, and the requirement that a solution be globally defined on the sphere. We derived a transformation (reflection) that creates a solution to Kundt’s constraint out of data defining an extremal isolated horizon. Using that transformation, we derived a class of exact solutions to the Einstein or Einstein–Maxwell equations of very special properties. Each spacetime we construct is foliated by a family of the Killing horizons. Moreover, it admits another, transversal Killing horizon. The intrinsic and extrinsic geometries of the transversal Killing horizon coincide with the one defined on the event horizon of the extremal Kerr–Newman solution. However, the Killing horizon in our example admits yet another Killing vector tangent to and null at it. The geometries of the leaves are given by the reflection.

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.