Showing papers by "Jerzy Lewandowski published in 2015"
TL;DR: In this paper, a scalar constraint operator for loop quantum gravity is defined on the recently introduced space of partially diffeomorphism invariant states, and this space is preserved by the action of the operator.
Abstract: We present a concrete and explicit construction of a new scalar constraint operator for loop quantum gravity. The operator is defined on the recently introduced space of partially diffeomorphism invariant states, and this space is preserved by the action of the operator. To define the Euclidean part of the scalar constraint operator, we propose a specific regularization based on the idea of so-called "special" loops. The Lorentzian part of the quantum scalar constraint is merely the curvature operator that has been introduced in an earlier work. Due to the properties of the special loops assignment, the adjoint operator of the non-symmetric constraint operator is densely defined on the partially diffeomorphism invariant Hilbert space. This fact opens up the possibility of defining a symmetric scalar constraint operator as a suitable combination of the original operator and its adjoint. We also show that the algebra of the scalar constraint operators is anomaly free, and describe the structure of the kernel of these operators on a general level.
58 citations
TL;DR: In this article, the authors describe a general mechanism for emergence of a rainbow metric from a quantum cosmological model, based on QFT on a quantum spacetime, whose metric depends explicitly on the energy of the field.
51 citations
TL;DR: In this paper, the authors present the construction of a physical Hamiltonian operator in the deparametrized model of loop quantum gravity coupled to a free scalar field, based on the use of the recently introduced curvature operator, and on the idea of so-called "special loops".
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.
50 citations
TL;DR: In this paper, the authors define a new Hilbert space of states which are solutions of a large number of components of the diffeomorphism constraint and obtain a family of gravitational scalar constraints.
Abstract: In the framework of loop quantum gravity, we define a new Hilbert space of states which are solutions of a large number of components of the diffeomorphism constraint. On this Hilbert space, using the methods of Thiemann, we obtain a family of gravitational scalar constraints. They preserve the Hilbert space for every choice of lapse function. Thus adjointness and commutator properties of the constraint can be investigated in a straightforward manner. We show how the space of solutions of the symmetrized constraint can be defined by spectral decomposition, and the Hilbert space of physical states by subsequently fully implementing the diffeomorphism constraint. The relationship of the solutions to those resulting from a proposal for a symmetric constraint operator by Thiemann remains to be elucidated.
37 citations
TL;DR: In this paper, the authors present a reformulation of the standard canonical approach to spherically symmetric systems in which the radial gauge is imposed, and apply the same techniques to the full theory, without assuming spherical symmetry, resulting in a reduced phase space description of General Relativity.
Abstract: Firstly, we present a reformulation of the standard canonical approach to spherically symmetric systems in which the radial gauge is imposed. This is done via the gauge unfixing techniques, which serves as their exposition in the context of the radial gauge. Secondly, we apply the same techniques to the full theory, without assuming spherical symmetry, resulting in a reduced phase space description of General Relativity. The canonical structure of the theory is analysed. In a companion paper a quantization of the reduced phase space is presented. The construction is well suited for the treatment of spherically symmetric situations and allows for a quantum definition thereof.
31 citations
TL;DR: In this paper, the authors propose two distinct quantum reductions to spherical symmetry within full 3 + 1 -dimensional loop quantum gravity, based on a purely geometric construction of observables for the spatial diffeomorphism constraint.
29 citations
TL;DR: In this paper, a scalar field can serve as a time variable during dynamical evolution of the matter-geometry system, especially in regions of high curvature, which are essential from the perspective of quantum gravity.
Abstract: Using a scalar field as an intrinsic 'clock' while investigating the dynamics of gravitational systems has been successfully pursued in various researches on the border between classical and quantum gravity. The objective of our research was to check explicitly whether the scalar field can serve as a time variable during dynamical evolution of the matter-geometry system, especially in regions of high curvature, which are essential from the perspective of quantum gravity. For this purpose, we analyzed a gravitational collapse of a self-interacting scalar field within the framework of general relativity. The obtained results indicated that the hypersurfaces of constant scalar field are spacelike in dynamical regions nearby the singularities formed during the investigated process. The scalar field values change monotonically in the areas, in which the constancy hypersurfaces are spacelike.
16 citations
TL;DR: In this paper, the heat kernel coherent states of Hall and Thiemann were used to construct operators corresponding to functions depending on holonomies and fluxes associated to a fixed graph.
Abstract: We present a new method for constructing operators in loop quantum gravity. The construction is an application of the general idea of "coherent state quantization", which allows one to associate a unique quantum operator to every function on a classical phase space. Using the heat kernel coherent states of Hall and Thiemann, we show how to construct operators corresponding to functions depending on holonomies and fluxes associated to a fixed graph. We construct the coherent state versions of the fundamental holonomy and flux operators, as well as the basic geometric operators of area, angle and volume. Our calculations show that the corresponding canonical operators are recovered from the coherent state operators in the limit of large spins.
9 citations
TL;DR: In this paper, it was shown that the algebra of the observables F(r, θ) is simpler than it was described in [1] and that an important subalgebra becomes canonical, allowing for a natural reduction of the phase space.
Abstract: In this addendum we clarify a point which strengthens one of the results from [1]. Namely, we show that the algebra of the observables F(r, θ) is yet simpler then it was described in [1]. This is an important point, because with this simplification an important subalgebra becomes canonical, allowing for a natural reduction of the phase space.
8 citations
TL;DR: In this article, the canonical structure of a spacetime version of the radial gauge was discussed and it was shown that the involved Dirac bracket is inherently non-local in the sense that no complete set of observables can be found which is constructed locally and at the same time has local Dirac brackets.
Abstract: We discuss the canonical structure of a spacetime version of the radial gauge, i.e. Gau{\ss}ian normal spacetime coordinates. While it was found for the spatial version of the radial gauge that a "local" algebra of observables can be constructed, it turns out that this is not possible for the spacetime version. The technical reason for this observation is that the new gauge condition needed to upgrade the spatial to a spacetime radial gauge does not Poisson-commute with the previous gauge conditions. It follows that the involved Dirac bracket is inherently non-local in the sense that no complete set of observables can be found which is constructed locally and at the same time has local Dirac brackets. A locally constructed observable here is defined as a finite polynomial of the canonical variables at a given physical point specified by the Gau{\ss}ian normal spacetime coordinates.
7 citations
TL;DR: In this paper, it was shown that the algebra of the observables $F(r,\theta) is simpler than it was described in [the original paper] and that an important subalgebra becomes canonical, allowing a natural reduction of the phase space.
Abstract: In this addendum we clarify a point which strengthens one of the results from [the original paper]. Namely, we show that the algebra of the observables $F(r,\theta)$ is yet simpler then it was described in [the original paper]. This is an important point, because with this simplification an important subalgebra becomes canonical, allowing for a natural reduction of the phase space.