arXiv subjects

Jakub Bilski

Publications and source records attributed to Jakub Bilski.

15 recordsLinked to original sources

arXiv2024

A comparative analysis of deep learning models for lung segmentation on X-ray images

Robust and highly accurate lung segmentation in X-rays is crucial in medical imaging. This study evaluates deep learning solutions for this task, ranking existing methods and analyzing their performance under diverse image modifications. Out of 61 analyzed papers, only nine offered implementation or pre-trained models, enabling assessment of three prominent methods: Lung VAE, TransResUNet, and CE-Net. The analysis revealed that CE-Net performs best, demonstrating the highest values in dice similarity coefficient and intersection over union metric.

eess.IV↗

arXiv2021

New Massive JT Multi-Gravity and N-Replica of SYK Models

We study a series of powerful correspondences among new multi-gravity extensions of the Jackiw-Teitelboim model, multi-SYK models and multi-Schwarzian quantum mechanics, in the $\rm{(A)dS_{2}/CFT}$ arena. Deploying a $BF$-like formulation of the model, we discuss the counting of the degrees of freedom for some specific classes of multi-gravity potentials, and unveil connections among a variety of apparently different models. Quantization of multi-gravity models can be then achieved from both the Hartle-Hawking no-boundary proposal, the SYK partition function and the spin-foam approaches. We comment on the SYK quantization procedure, and deepen in the appendix the quantization scheme naturally achieved in the $BF$ framework. The new multi-gravity theory hence recovered presents intriguing applications for analogue gravitational models developed for condensed matter physics, including graphene, endowed with defects and high intensity magnetic fields.

hep-th↗

arXiv2021

Implementation of the holonomy representation of the Ashtekar connection in loop quantum gravity

The improved lattice regularization method of the Ashtekar connection holonomy representation in loop quantum gravity is described in this article. The approach is based on the geometric expansion of holonomies into power series up to the quadratic order terms in the regularization parameter. As a result, a more accurate procedure than the currently established approach to the canonical lattice quantization of gravity is obtained. Moreover, if holonomies are defined along linear links, this procedure becomes exact. Furthermore, in the improved method, the symmetry of holonomies assigned to links is directly reflected in the related distribution of connections. Finally, the domain of the lattice-regularized Hamiltonian constraint takes a natural structure of elementary cells sum. Consequently, under certain restrictions, the related scalar constraint operator, which spectrum is independent of intertwiners, can be defined.

gr-qc↗

arXiv2021

Lattice classical cosmology

This article presents the lattice-smeared gravity phase space reduction defined by the cosmological gauge-fixing conditions. These conditions are specified to reduce the SU(2) symmetry and the spatial diffeomorphism invariance of the loop quantum gravity's Fock space, known as the spin network. The internal symmetry is fixed to the Abelian case and the diffeomorphism invariance is simultaneously reduced to spatial translations. The unification of the results of the related gauge fixing conditions leads to the gauge generators correlation. Consequently, these conditions become solvable by constant variables; hence the reduced constraints become globally satisfied and vanish identically. By rigorously satisfying the reduced gauge symmetries, the resulting cosmological model is precisely the limit of the gravitational theory expressed in terms of holonomies and fluxes. Moreover, the obtained Hamiltonian constraint is finite (without any cut-off introduction) and as rigorous as an approximation of a Lie group by its representation. Furthermore, it has the form of the sum over elementary cuboidal cells. Finally, the simple structure of its homogeneities and anisotropies should allow to describe the quantum cosmological evolution of the Universe in terms of transition amplitudes, instead of using perturbative approximations.

gr-qc↗

arXiv2021

Relativistic classical theory II. Holonomy-flux representation of gravitational degrees of freedom

This article describes the regularization of the generally relativistic gauge field representation of gravity on a piecewise linear lattice. It is a part of the program concerning the classical relativistic theory of fundamental interactions, represented by minimally coupled gauge vector field densities and half-densities. The correspondence between the local Darboux coordinates on phase space and the local structure of the links of the lattice, embedded in the spatial manifold, is demonstrated. Thus, the canonical coordinates are replaceable by links-related quantities. This idea and the significant part of formalism are directly based on the model of canonical loop quantum gravity (CLQG). The first stage of this program is formulated regarding the gauge field, which dynamics is independent of other fundamental fields, but contributes to their dynamics. This gauge field, which determines systems equivalence in the actions defining all fundamental interactions, represents Einsteinian gravity. The related links-defined quantities depend on holonomies of gravitational connections and fluxes of densitized dreibeins. This article demonstrates how to determine these quantities, which lead to a nonpertubative formalism that preserves the general postulate of relativity. From this perspective, the formalism presented in this article is analogous to the Ashtekar-Barbero-Holst formulation on which CLQG is based. However, in this project, it is additionally required that the fields' coordinates are quantizable in the standard canonical procedure for a gauge theory and that any approximation in the construction of the model is at least as precisely demonstrated as the gauge invariance. These requirements lead to new relations between holonomies and connections, and the representation of the densitized deibein determinant that is more precise than the volume representation in CLQG.

gr-qc↗

arXiv2021

Regularization of the cosmological sector of loop quantum gravity with bosonic matter and the related problems with general covariance of quantum corrections

This article concerns the problems regarding different lattice regularization techniques for the matter fields of Hamiltonian constraints defined in the framework of loop quantum gravity. The analysis is formulated in the phase space-reduced cosmological model of the hypothetical theory of canonical quantum general relativity. This article explains why a different than links-related lattice smearing of fields leads to a local violation of general covariance. This happens by assuming, for instance, the nodes-related smearing. Therefore, this problem occurs in the case of any polymerlike scalar field quantization method by breaking the background independence of the semiclassical predictions. In consequence, the diffeomorphism symmetry that depends on a links distribution is broken locally at the level of generally relativistic corrections. Moreover, by using the phase space-reduced gauge fixing technique to analyze this issue, the results are general and they concern any coupling with the links-regularized gravitational degrees of freedom in loop quantum gravity. Therefore, they lead to the following no-go conclusion. Any lattice smearing of matter, not defined by using the geometrical distribution specified by the links-fluxes duality, violates the general principle of relativity.

gr-qc↗

arXiv2021

Lie algebra of Ashtekar-Barbero connection operators

Holonomies of the Ashtekar-Barbero connection can be considered as abstract elements of a Lie group exponentially mapped from their connections representation. This idea provides a possibility to compare the geometric and algebraic properties of these objects. The result allows to identify the next-to-the-leading-order terms in the geometric and algebraic expansion of a holonomy. This identification leads to the verification of the related Hilbert space formulation. If states are the representations of the holonomy's symmetry group, they preserve gauge transformations according to Wigner's theorem. Thus, the spin network in loop quantum gravity satisfies this theorem. Moreover, the considered identification of the different expansions ensures the reality of the Ashtekar connection. Only the holonomies of real connections lead to the formulation of states that satisfy Wigner's theorem.

gr-qc↗

arXiv2021

Continuously distributed holonomy-flux algebra

The procedure of the holonomy-flux algebra construction along a piecewise linear path, which consists of a countably infinite number of pieces, is described in this article. The related construction approximates the continuous distribution of the holonomy-flux algebra location along a smooth link arbitrarily well. The presented method requires the densitized dreibein flux and the corresponding operator redefinition. The derived result allows to formulate the gravitational Hamiltonian constraint regularization by applying the Thiemann technique adjusted to a piecewise linear lattice. By using the improved Ashtekar connection holonomy representation, which is more accurate than the one used in canonical loop quantum gravity, the corrections related to the redefined densitized dreibein flux vanish. In this latter case, the Poisson brackets of the continuously distributed holonomy-flux algebra along a link between a pair of nodes are equal to the brackets for these smeared variables located at the nodes.

gr-qc↗

arXiv2020

General-relativistic spin system

The models of spin systems defined on Euclidean space provide powerful machinery for studying a broad range of condensed matter phenomena. While the non-relativistic effective description is sufficient for most of the applications, it is interesting to consider special and general relativistic extensions of such models. Here, we introduce a framework that allows us to construct theories of continuous spin variables on a curved spacetime. Our approach takes advantage of the results of the non-linear field space theory, which shows how to construct compact phase space models, in particular for the spherical phase space of spin. Following the methodology corresponding to a bosonization of spin systems into the spin wave representations, we postulate a representation having the form of the Klein-Gordon field. This representation is equivalent to the semi-classical version of the well-known Holstein-Primakoff transformation. The general-relativistic extension of the spin wave representation is then performed, leading to the general-relativistically motivated modifications of the Ising model coupled to a transversal magnetic field. The advantage of our approach is its off-shell construction, while the popular methods of coupling fermions to general relativity usually depend on the form of Einstein field equations with matter. Furthermore, we show equivalence between the considered spin system and the Dirac-Born-Infeld type scalar field theory with a specific potential, which is also an example of k-essence theory. Based on this, the cosmological consequences of the introduced spin field matter content are preliminarily investigated.

hep-th↗

arXiv2020

Quantum Reduced Loop Gravity with matter: eigenvectors of the Hamiltonian operator in isotropic cosmology

Introducing a new method, we demonstrate how the action of reduced operators can be derived without resorting to a recoupling theory and how they exactly reproduce the results obtained in the standard approach of Quantum Reduced Loop Gravity (QRLG). This is particularly relevant while dealing with volume operator when dealing with the coupling of matter fields to gravity. Apart from reinforcing the close link between QRLG and loop quantum cosmology (LQC), this procedure also sheds new light on the issue of how to extract the continuum limit, without resorting to the large-$j$ expansion, thereby pointing towards a new approach to tackle this problem.

gr-qc↗

arXiv2020

Critical Insight into the Cosmological Sector of Loop Quantum Gravity

This article sheds new light on the problem of cosmological reduction in Loop Quantum Gravity. We critically analyze Quantum Reduced Loop Gravity -- an attempt to extract the cosmological sector of the full theory. We reconsider the reduction procedure applied to the states of the kinematical Hilbert space, developing a comparative analysis with previous efforts in the literature. We show that the constraints of the model were formerly instantiated in an inconsistent fashion, leading to an overconstrained dynamics and an ill-defined Hilbert space. We then scrutinize alternative implementations of symmetry-reduction. While remaining unaffected by the shortcomings encountered in Quantum Reduced Loop Gravity, these latter procedures bridge the gap between the full theory and former endeavors in Loop Quantum Cosmology.

gr-qc↗

arXiv2017

Klein-Gordon field from the XXZ Heisenberg model

We examine the recently introduced idea of Spin-Field Correspondence focusing on the example of the spin system described by the XXZ Heisenberg model with external magnetic field. The Hamiltonian of the resulting nonlinear scalar field theory is derived for arbitrary value of the anisotropy parameter $Δ$. We show that the linear scalar field theory is reconstructed in the large spin limit. For $Δ=1$ a non-relativistic scalar field theory satisfying the Born reciprocity principle is recovered. As expected, for the vanishing anisotropy parameter $Δ\rightarrow 0$ the standard relativistic Klein-Gordon field is obtained. Various aspects of the obtained class of the scalar fields are studied, including the fate of the relativistic symmetries and the properties of the emerging interaction terms. We show that, in a certain limit, the so-called polymer quantisation of the field variables is recovered. This and other discussed properties suggest a possible relevance of the considered framework in the context of quantum gravity.

hep-th↗

arXiv2017

2+1 homogeneous Loop Quantum Gravity with a scalar field clock

We focus on three-dimensional QRLG with the purpose of shedding light on the link between reduced LQG and LQC in four space-time dimensions. Considering homogeneous three-dimensional LQG, the theory simplifies to QRLG. We then implement Thiemann's Quantum Spin Dynamics for Euclidean three-dimensional space-time in presence of a real scalar matter field. We deploy a polymer quantization of the scalar field while using methods of quantum reduced loop gravity. We compute the scalar Hamiltonian operator on the states of the kinematical Hilbert space of the theory, and exhibit its matrix elements that are derived using a new simplified method. The coupling to matter, which plays the role of a carrier of dynamics, opens the pathway to the study of phenomenological implications. We finally comment on the relations between three-dimensional QRLG and LQC, as well as on the appearance of the correspondence principle for the scalar field.

gr-qc↗

arXiv2016

Quantum reduced loop gravity: extension to gauge vector field

Within the framework of Quantum Reduced Loop Gravity we quantize the Hamiltonian for a gauge vector field. The regularization can be performed using tools analogous to the ones adopted in full Loop Quantum Gravity, while the matrix elements of the resulting operator between basis states are analytic coefficients. This analysis is the first step towards deriving the full quantum gravity corrections to the vector field semiclassical dynamics.

gr-qc↗

arXiv2015

Quantum reduced loop gravity: extension to scalar field

The quantization of the Hamiltonian for a scalar field is performed in the framework of Quantum Reduced Loop Gravity. We outline how the regularization can be performed by using the analogous tools adopted in full Loop Quantum Gravity and the matrix elements of the resulting operator between basis states are analytic coefficients. These achievements open the way for a consistent analysis of the Quantum Gravity corrections to the classical dynamics of gravity in the presence of a scalar field in a cosmological setting.

gr-qc↗