arXiv subjects

Dine Ousmane Samary

Publications and source records attributed to Dine Ousmane Samary.

At least 55 records · Page 3Linked to original sources

arXiv2021

Field theoretical approach for signal detection in nearly continuous positive spectra II: Tensorial data

The tensorial principal component analysis is a generalization of ordinary principal component analysis, focusing on data which are suitably described by tensors rather than matrices. This paper aims at giving the nonperturbative renormalization group formalism based on a slight generalization of the covariance matrix, to investigate signal detection for the difficult issue of nearly continuous spectra. Renormalization group allows constructing effective description keeping only relevant features in the low ``energy'' (i.e. large eigenvalues) limit and thus provides universal descriptions allowing to associate the presence of the signal with objectives and computable quantities. Among them, in this paper, we focus on the vacuum expectation value. We exhibit experimental evidence in favor of a connection between symmetry breaking and the existence of an intrinsic detection threshold, in agreement with our conclusions for matrices, providing a new step in the direction of a universal statement.

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arXiv2021

Signal detection in nearly continuous spectra and symmetry breaking

The large scale behavior of systems having a large number of interacting degrees of freedom is suitably described using renormalization group, from non-Gaussian distributions. Renormalization group techniques used in physics are then expected to be helpful for issues when standard methods in data analysis break down. Signal detection and recognition for covariance matrices having nearly continuous spectra is currently an open issue in data science and machine learning. Using the field theoretical embedding introduced in arXiv:2011.02376 to reproduces experimental correlations, we show in this paper that the presence of a signal may be characterized by a phase transition with $\mathbb{Z}_2$-symmetry breaking. For our investigations, we use the nonperturbative renormalization group formalism, using a local potential approximation to construct an approximate solution of the flow. Moreover, we focus on the nearly continuous signal build as a perturbation of the Marchenko-Pastur law with many discrete spikes.

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arXiv2021

Generalized scale behavior and renormalization group for data analysis

Some recent results showed that renormalization group can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis for the case of large dimensional data sets with covariance having a nearly continuous spectrum. In this case, the distinction between "noise-like" and "non-noise" modes becomes arbitrary and an open challenge for standard methods. Observing that both renormalization group and principal component analysis search for simplification for systems involving many degrees of freedom, we aim to use the renormalization group argument to clarify the turning point between noise and information modes. The analogy between coarse-graining renormalization and principal component analysis has been investigated in [Journal of Statistical Physics,167, Issue 3-4, pp 462-475, (2017)], from a perturbative framework, and the implementation with real sets of data by the same authors showed that the procedure may reflect more than a simple formal analogy. In particular, the separation of sampling noise modes may be controlled by a non-Gaussian fixed point, reminiscent of the behaviour of critical systems. In our analysis, we go beyond the perturbative framework using nonperturbative techniques to investigate non-Gaussian fixed points and propose a deeper formalism allowing going beyond power-law assumptions for explicit computations.

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arXiv2020

Ward-constrained melonic renormalization group flow for the rank-four $ϕ^6$ tensorial group field theory

The nontrivial fixed point discovered for $ϕ^4$-marginal couplings in tensorial group field theories have been showed to be incompatible with Ward-Takahashi identities. In this previous analysis we have stated that the case of models with interactions of order greater than four could probably lead to a fixed point compatible with local Ward's identities. In this paper we focus on a rank-4 Abelian $ϕ^6$-just renormalizable tensorial group field theory and describe the renormalization group flow over the sub-theory space where Ward constraint is satisfied along the flow, by using an improved version of the effective vertex expansion. We show that this model exhibit a nontrivial fixed points in this constrained subspace. Finally, the well-known asymptotically freedom of this model is highlighted.

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arXiv2020

Renormalization group flow of coupled tensorial group field theories: Towards the Ising model on random lattices

We introduce a new family of tensorial field theories by coupling different fields in a non-trivial way, with a view towards the investigation of the coupling between matter and gravity in the quantum regime. As a first step, we consider the simple case with two tensors of the same rank coupled together, with Dirac like kinetic kernel. We focus especially on rank-$3$ tensors, which lead to a power counting just-renormalizable model, and interpret Feynman graphs as Ising configurations on random lattices. We investigate the renormalization group flow for this model, using two different and complementary tools for approximations, namely, the effective vertex expansion method and finite-dimensional truncations for the flowing action. Due to the complicated structure of the resulting flow equations, we divided the work into two parts. In this first part we only investigate the fundamental aspects on the construction of the model and the different ways to get tractable renormalization group equations, while their numerical analysis will be addressed in a companion paper.

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arXiv2019

Ward identity violation for melonic $T^4$-truncation

Referring to recent works concerning the functional renormalization group for tensorial group fields theories [arXiv:1803.09902] and [arXiv:1809.00247], this paper gives in-depth explanation for, the ambiguity around the search of fixed points in the Wetterich flow equation and the Ward-Takahashi identities. We consider the $U(1)$-tensors models and discuss the non-existence of phase transition taking into account the Ward-identities as new constraint along the flow. We prove that the quartic melonic tensorial group fields theories without closure constraint are devoid with the fixed points and therefore the phase transitions.

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arXiv2019

Progress in the solving nonperturbative renormalization group for tensorial group field theory

This manuscript aims at giving our new advance on the functional renormalization group applied to tensorial group field theory. It is based on a series of our three papers [arXiv:1803.09902], [arXiv:1809.00247] and [arXiv:1809.06081]. We consider the polynomial Abelian $U(1)^d$ models without closure constraint, especially we discuss the case of quartic melonic interaction. We present a new approach to solve the exact Wetterich flow equation called the effective vertex expansion method, and investigate the resulting flow equations, especially about the existence of non-Gaussian fixed points for their connection with phase transitions. To complete this method, we consider a non-trivial constraint arising from the Ward-Takahashi identities, and discuss the disappearance of the global non-trivial fixed points taking into account this constraint. Finally, we argue in favor of an alternative scenario involving a phase transition into the reduced phase space given by the Ward constraint.

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arXiv2019

Unitary symmetry constraints on tensorial group field theory renormalization group flow

Renormalization group methods are an essential ingredient in the study of nonperturbative problems of quantum field theory. This paper deal with the symmetry constraints on the renormalization group flow for quartic melonic tensorial group field theories. Using the unitary invariance of the interactions, we provide a set of Ward-Takahashi identities which leads to relations between correlation functions. There are numerous reasons to consider such Ward identities in the functional renormalization group. Their compatibility along the flow provides a non-trivial constraint on the reliability of the approximation schemes used in the non-perturbative regime, especially on the truncation and the choice of the regulator. We establish the so called structure equations in the melonic sector and in the symmetric phase. As an example we consider the $T^4_5$ TGFT model without gauge constraint. The Wetterich flow equation is given and the way to improve the truncation on the effective action is also scrutinized.

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arXiv2019

Ward-constrained melonic renormalization group flow

In recent years, some interesting investigations of the non-perturbative renormalization group equations for tensorial group field theories have been done in the truncation method, and completely discarding the Ward identities from their analysis. In this letter, in continuation of our recent series of papers, we present a new framework of investigation, namely the effective vertex expansion, allowing to consider infinite sectors rather than finite dimensional subspaces of the full theory space. We focus on the ultraviolet behavior, and provide a new and complete description of the renormalization group flow constrained with Ward identities.

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arXiv2019

Lattice oscillator model on noncommutative space: eigenvalues problem for the perturbation theory

Harmonic oscillator in noncommutative two dimensional lattice are investigated. Using the properties of non-differential calculus and its applications to quantum mechanics, we provide the eigenvalues and eigenfunctions of the corresponding Hamiltonian. First we consider the case of ordinary quantum mechanics, and we point out the thermodynamic properties of the model. Then we consider the same question when both coordinates and momentums are noncommutative.

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arXiv2018

Energy momentum tensor for translation invariant renormalizable noncommutative field theory

In this paper, we derive the energy momentum tensor for the translation invariant noncommutative Tanasa scalar field model. The Wilson regularization procedure is used to improve this tensor and the local conservation property is recovered. The same question is addressed in the case where the Moyal star product is deformed including the tetrad fields. It provides with an extension of the recent work [J. Phys. A: Math. Theor. 43 (2010) 155202], regarding the computation and properties of the Noether currents to the renormalizable models.

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arXiv2017

Functional renormalization group for the $U(1)$-$T_5^6$ tensorial group field theory with closure constraint

This paper is focused on the functional renormalization group applied to the $T_5^6$ tensor model on the Abelian group $U(1)$ with closure constraint. For the first time, we derive the flow equations for the couplings and mass parameters in a suitable truncation around the marginal interactions with respect to the perturbative power counting. For the second time, we study the behavior around the Gaussian fixed point, and show that the theory is nonasymptotically free. Finally, we discuss the UV completion of the theory. We show the existence of several nontrivial fixed points, study the behavior of the renormalization group flow around them, and point out evidence in favor of an asymptotically safe theory.

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arXiv2017

Noncommutative Dirac and Klein-Gordon oscillators in the background of cosmic string: spectrum and dynamics

From a study of an oscillator in a $4D$ NC spacetime, we establish the Hamilton equations of motion. The formers are solved to give the oscillator position and momentum coordinates. These coordinates are used to build a metric similar to that describing a cosmic string. On this basis, Dirac and Klein-Gordon oscillators are investigated. Their spectrum and dynamics are analysed giving rise to novel interesting properties.

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arXiv2016

Spherically symmetric potential in noncommutative spacetime with a compactified extra dimensions

The Schrödinger equation of the spherical symmetry quantum models such as the hydrogen atom problem seems to be analytically non-solvable in higher dimensions. When we try to compactifying one or several dimensions this question can maybe solved. This paper stands for the study of the spherical symmetry quantum models on noncommutative spacetime with compactified extra dimensions. We provide analytically the resulting spectrum of the hydrogen atom and Yukawa problem in $4+1$ dimensional noncommutative spacetime in the first order approximation of noncommutative parameter. The case of higher dimensions $D\geq 4$ is also discussed.

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arXiv2015

Production of Dirac particle in a deformed Minkowsky space-time

In this paper we study the Dirac field theory interacting with external gravitation field, described with tetrad of the form $e_b^μ(x)=\varepsilon(δ_b^μ+ω_{ba}^μx^a)$, where $\varepsilon=1$ for $μ=0$ and $\varepsilon=i$ for $μ=1,2,3.$ The probability density of the vacuum-vacuum pair creation is given. In particular case of vanishing electromagnetic fields, we point out how this deformation modify the amplitude transition. The corresponding Dirac equation is solved.

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arXiv2015

Correlation functions of just renormalizable tensorial group field theory: The melonic approximation

The $D$-colored version of tensor models has been shown to admit a large $N$-limit expansion. The leading contributions result from so-called melonic graphs which are dual to the $D$-sphere. This is a note about the Schwinger-Dyson equations of the tensorial $φ^{4}_{5}$-model (with propagator $1/{\bf p}^{2}$) and their melonic approximation. We derive the master equations for two- and four-point correlation functions and discuss their solution.

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arXiv2015

Pair production of Dirac particles in a d+1-dimensional noncommutative space-time

This work addresses the computation of the propability of fermionic particle pair production in $(d+1)-$ dimensional noncommutative Moyal space. Using the Seiberg-Witten maps that establish relations between noncommutative and commutative field variables, to first order in the noncommutative parameter $θ$, we derive the probability density of vacuum-vacuum pair production of Dirac particles. The cases of constant electromagnetic, alternating time-dependent and space-dependent electric fields are considered and discussed.

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arXiv2014

Position-dependent noncommutative quantum models: Exact solution of the harmonic oscillator

This paper is devoted to find the exact solution of the harmonic oscillator in a position-dependent 4-dimensional noncommutative phase space. The noncommutative phase space that we consider is described by the commutation relations between coordinates and momenta: $[\hat{x}^1,\hat{x}^2]=iθ(1+ω_2 \hat x^2)$, $[\hat{p}^1,\hat{p}^2]=i\barθ$, $[\hat{x}^i,\hat{p}^j]=i\hbar_{eff}δ^{ij}$. We give an analytical method to solve the eigenvalue problem of the harmonic oscillator within this deformation algebra.

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