Author
Jerzy Lewandowski
Other affiliations: University of Florida, Syracuse University, Beijing Normal University ...read more
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.
Papers published on a yearly basis
Papers
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TL;DR: 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 as discussed by the authors.
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 noncommutative C*-algebra defining a compact quantum group.
6 citations
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TL;DR: In this paper, a generalized Raychaudhuri equation for nonexpanding null surfaces in arbitrarily dimensional case is proposed and the geometry of a vacuum isolated horizon is determined by the induced metric and the rotation 1-form potential, local generalizations of the area and angular momentum typically used in the stationary black hole solutions case.
Abstract: With a help of a generalized Raychaudhuri equation non-expanding null surfaces are studied in arbitrarily dimensional case. The definition and basic properties of non-expanding and isolated horizons known in the literature in the 4 and 3 dimensional cases are generalized. A local description of horizon's geometry is provided. The Zeroth Law of black hole thermodynamics is derived. The constraints have a similar structure to that of the 4 dimensional spacetime case. The geometry of a vacuum isolated horizon is determined by the induced metric and the rotation 1-form potential, local generalizations of the area and the angular momentum typically used in the stationary black hole solutions case.
6 citations
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TL;DR: In this article, the degenerate Ashtekar -Einstein equations were solved by suitable gauge fixing and choice of coordinates for degenerate data, and the remaining degenerate sectors of the classical (3 + 1)-dimensional theory were considered.
Abstract: This work completes the task of solving locally the Einstein - Ashtekar equations for degenerate data. The two remaining degenerate sectors of the classical (3 + 1)-dimensional theory are considered. First, with all densitized triad vectors linearly dependent and second, with only two independent ones. It is shown how to solve the Ashtekar - Einstein equations completely by suitable gauge fixing and choice of coordinates. Remarkably, the Hamiltonian weakly Poisson commutes with the conditions defining the sectors. The summary of degenerate solutions is given in an appendix.
5 citations
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TL;DR: In this paper, the volume operator of loop quantum cosmology and all its positive powers are shown to be ill-defined on physical states, and it was recently shown that almost every step in the procedure is illdefined and relies heavily upon a (seemingly premature) numerical truncation.
Abstract: It was recently shown that the volume operator of loop quantum cosmology (LQC) and all its positive powers are ill-defined on physical states. In this paper, we investigate how it effects predictions of cosmic microwave background (CMB) power spectra obtained within dressed metric approach for which expectations values of $\hat{a}$ are the key element. We find that almost every step in the procedure is ill-defined and relies heavily upon a (seemingly premature) numerical truncation. Thus, it suggests that more care is needed in making predictions regarding pre-inflationary physics. We propose a new scheme which contains only well-defined quantities. The surprising agreement of the hitherto models with observational data, especially at low angular momenta $l$ is explained.
5 citations
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TL;DR: In particular, theories with uncountably many non-vanishing Wilson-loop expectation values cannot be gained this way as mentioned in this paper, and it is shown that the definition of physical integration measures via exponential of minus the action times kinematical integration measure typically contradicts properties of physical models.
Abstract: Max-Planck-Institut fu¨r Gravitationsphysik, Albert-Einstein-Institut, Am Mu¨hlenberg 1, 14476 Golm, Germany(October 31, 2001)It is shown that the definition of physical integration measures via “exponential of minus theaction times kinematical integration measure” typically contradicts properties of physical models.In particular, theories with uncountably many non-vanishing Wilson-loop expectation values cannotbe gained this way. The results are rigorous within the Ashtekar approach to gauge field theories.PACS: 11.15.Tk, 02.30.Cj MSC 2000: 81T13; 81T27, 28C20, 58D20Introduction
5 citations
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28,685 citations
01 Dec 1982
1,915 citations
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TL;DR: Loop quantum gravity as discussed by the authors is a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry.
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.
1,804 citations
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TL;DR: In this article, an improved Hamiltonian constraint operator is introduced in loop quantum cosmology for the isotropic model with a massless scalar field and the big bang is replaced by a quantum bounce.
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.
1,171 citations
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TL;DR: Loop quantum cosmology (LQC) as mentioned in this paper is the result of applying principles of loop quantum gravity to cosmological settings, where 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.
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.
1,162 citations