arXiv subjects

Olivier Piguet

Publications and source records attributed to Olivier Piguet.

At least 19 recordsLinked to original sources

arXiv2025

Spin One Matter Fields

It is shown how spin one vector matter fields can be coupled to a Yang-Mills theory. Such matter fields are defined as belonging to a representation $R$ of this Yang-Mills gauge algebra $\mathfrak{g}$. It is also required that these fields together with the original gauge fields be the gauge fields of an embedding total gauge algebra $\mathfrak{g}_{\rm tot}$. The existence of a physically consistent Yang-Mills action for the total algebra is finally required. These conditions are rather restrictive, as shown in some examples: non-trivial solutions may or may not exist depending on the choice of the original algebra $\mathfrak{g}$ and of the representation $R$. Some examples are shown, the case of the initial algebra $\mathfrak{g}$ = $\mathfrak{u}(1)\oplus\mathfrak{su}(2)$ being treated in more detail.

hep-th↗

arXiv2023

Bohm - de Broglie Cycles

In the de Broglie-Bohm quantum theory, particles describe trajectories determined by the flux associated with their wave function. These trajectories are studied here for relativistic spin-one-half particles.Based in explicit numerical calculations for the case of a massless particle in dimension three space-time, it is shown that if the wave function is an eigenfunction of the total angular momentum, the trajectories begin as circles of slowly increasing radius until a transition time at which they tend to follow straight lines. Arrival times at some detector, as well as their probability distribution are calculated, too. The chosen energy and momentum parameters are of the orders of magnitude met in graphene's physics.

quant-ph↗

arXiv2020

Five dimensional Chern-Simons Gravity for the expanded (anti)-de Sitter gauge group C$_5$

We study the Hamiltonian dynamics of a five-dimensional Chern-Simons theory for the gauge algebra $C_5$ of Izaurieta, Rodriguez and Salgado, the so-called S$_H$-expansion of the 5D (anti-)de Sitter algebra (a)ds, based on the cyclic group $\mathbb{Z}_4$. The theory consists of a 1-form field containing the (a)ds gravitation variables and 1-form field transforming in the adjoint representation of (a)ds. The gravitational part of the action necessarily contains a term quadratic in the curvature, beyond the Einstein-Hilbert and cosmological terms, for any choice of the two independent coupling constants. The total action is also invariant under a new local symmetry, called "crossed diffeomorphisms", beyond the usual space-time diffeomorphisms. The number of physical degrees of freedom is computed. The theory is shown to be "generic" in the sense of Bañados, Garay and Henneaux, i.e., the constraint associated to the time diffeomorphisms is not independent from the other constraints.

gr-qc↗

arXiv2019

Quantum Charged Spinning Massless Particles in 2+1 dimensions

Motivated by the conduction properties of graphene discovered and studied in the last decades, we consider the quantum dynamics of a massless, charged, spin 1/2 relativistic particle in three dimensional space-time, in the presence of an electrostatic field in various configurations such as step or barrier potentials and generalizations of them. The field is taken as parallel to the y coordinate axis and vanishing outside of a band parallel to the x axis. The classical theory is reviewed, together with its canonical quantization leading to the Dirac equation for a 2-component spinor. Stationary solutions are numerically found for each of the field configurations considered, fromwhich we calculate the mean quantum trajectories of the particle and compare them with the corresponding classical trajectories, the latter showing a classical version of the Klein phenomenon. Transmission and reflection probabilities are also calculated, confirming the Klein phenomenon.

hep-th↗

arXiv2017

Behaviour of Charged Spinning Massless Particles

We revisit the classical theory of a relativistic massless charged point particle with spin and interacting with an external electromagnetic field. In particular, we give a proper definition of its kinetic energy and its total energy, the latter being conserved when the external field is stationary. We also write the conservation laws for the linear and angular momenta. Finally, we find that the particle's velocity may differ from $c$ as a result of the spin---electromagnetic field interaction, without jeopardizing Lorentz invariance.

hep-th↗

arXiv2017

Idea density for predicting Alzheimer's disease from transcribed speech

Idea Density (ID) measures the rate at which ideas or elementary predications are expressed in an utterance or in a text. Lower ID is found to be associated with an increased risk of developing Alzheimer's disease (AD) (Snowdon et al., 1996; Engelman et al., 2010). ID has been used in two different versions: propositional idea density (PID) counts the expressed ideas and can be applied to any text while semantic idea density (SID) counts pre-defined information content units and is naturally more applicable to normative domains, such as picture description tasks. In this paper, we develop DEPID, a novel dependency-based method for computing PID, and its version DEPID-R that enables to exclude repeating ideas---a feature characteristic to AD speech. We conduct the first comparison of automatically extracted PID and SID in the diagnostic classification task on two different AD datasets covering both closed-topic and free-recall domains. While SID performs better on the normative dataset, adding PID leads to a small but significant improvement (+1.7 F-score). On the free-topic dataset, PID performs better than SID as expected (77.6 vs 72.3 in F-score) but adding the features derived from the word embedding clustering underlying the automatic SID increases the results considerably, leading to an F-score of 84.8.

cs.CL↗

arXiv2017

Chern-Simons Gravity in Four Dimensions

Five dimensional Chern-Simons theory with (anti-)de Sitter SO(1,5) or SO(2,4) gauge invariance presents an alternative to General Relativity with cosmological constant. We consider the zero-modes of its Kaluza-Klein compactification to four dimensions. Solutions with vanishing torsion are obtained in the cases of a spherically symmetric 3-space and of a homogeneous and isotropic 3-space, which reproduce the Schwarzshild-de Sitter and $Λ$CDM cosmological solutions of General Relativity. We also check that vanishing torsion is a stable feature of the solutions.

gr-qc↗

arXiv2016

Dimensionally compactified Chern-Simon theory in 5D as a gravitation theory in 4D

We propose a gravitation theory in 4 dimensional space-time obtained by compacting to 4 dimensions the five dimensional topological Chern-Simons theory with the gauge group SO(1,5) or SO(2,4) -- the de Sitter or anti-de Sitter group of 5-dimensional space-time. In the resulting theory, torsion, which is solution of the field equations as in any gravitation theory in the first order formalism, is not necessarily zero. However, a cosmological solution with zero torsion exists, which reproduces the Lambda-CDM cosmological solution of General Relativity. A realistic solution with spherical symmetry is also obtained.

gr-qc↗

arXiv2016

A Topological-like Model for Gravity in 4D Space-time

In this paper we consider a model for gravity in 4-dimensional space-time originally proposed by Chamseddine, which may be derived by dimensional reduction and truncation from a 5-dimensional Chern-Simons theory. Its topological origin makes it an interesting candidate for an easier quantization, e.g., in the Loop Quantization framework. The present paper is dedicated to a classical analysis of the model's properties. Cosmological solutions as well as wave solutions are found and compared with the corresponding solutions of Einstein's General Relativity with cosmological constant.

gr-qc↗

arXiv2016

Symanzik-Becchi-Rouet-Stora lessons on renormalizable models with broken symmetry: the case of Lorentz violation

In this paper, we revisit the issue intensively studied in recent years on the generation of terms by radiative corrections in models with broken Lorentz symmetry. The algebraic perturbative method of handling the problem of renormalization of the theories with Lorentz symmetry breaking, is used. We hope to make clear the Symanzik's aphorism: "{\it Whether you like it or not, you have to include in the lagrangian all counter terms consistent with locality and power-counting, unless otherwise constrained by Ward identities.}"

hep-th↗

arXiv2014

Reduction of couplings and its application in particle physics, Finite theories, Higgs and top mass predictions

In this report we tell the story of the notion "reduction of couplings" as we witnessed it in the course of time. Born as an innocent child of renormalization theory it first served the study of asymptotic behavior of several couplings in a given model. Reduced couplings appeared as functions of a primary one, compatible with the renormalization group equation and thus solutions of a specific set of ordinary differential equations. If these functions have the form of power series the respective theories resemble standard renormalizable ones and thus widen considerably the area covered until then by symmetries as a tool for constraining the number of couplings consistently. Still on the more abstract level reducing couplings enabled one to construct theories with beta-functions vanishing to all orders of perturbation theory. Reduction of couplings became physicswise truely interesting and phenomenologically important when applied to the standard model and its possible extensions. In particular in the context of supersymmetric theories it became the most powerful tool known today once it was learned how to apply it also to couplings having dimension of mass and to mass parameters. Technically this all relies on the basic property that reducing couplings is a renormalization scheme independent procedure. Predictions of top and Higgs mass prior to their experimental finding highlight the fundamental physical significance of this notion. Twenty-two original articles and one set of lectures are being commented, put into historical perspective and interrelated with each other.

hep-ph↗

arXiv2014

Loop quantization of a 3D Abelian BF model with sigma-model matter

The main goal of this work is to explore the symmetries and develop the dynamics associated to a 3D Abelian BF model coupled to scalar fields submitted to a sigma model like constraint, at the classical and quantum levels. We apply to the present model the techniques of Loop Quantum Gravity, construct its physical Hilbert space and its observables.

gr-qc↗

arXiv2014

Loop Quantization of a Model for D=1+2 (Anti)de Sitter Gravity Coupled to Topological Matter

We present a complete quantization of Lorentzian D=1+2 gravity with cosmological constant, coupled to a set of topological matter fields. The approach of Loop Quantum Gravity is used thanks to a partial gauge fixing leaving a residual gauge invariance under a compact semi-simple gauge group, namely Spin(4) = SU(2) x SU(2). A pair of quantum observables is constructed, which are non-trivial despite of being null at the classical level.

gr-qc↗

arXiv2012

Complete loop quantization of a dimension 1+2 Lorentzian gravity theory

De Sitter Chern-Simons gravity in D = 1 + 2 spacetime is known to possess an extension with a Barbero-Immirzi like parameter. We find a partial gauge fixing which leaves a compact residual gauge group, namely SU(2). The compacticity of the residual gauge group opens the way to the usual LQG quantization techniques. We recall the exemple of the LQG quantization of SU(2) CS theory with cylindrical space topology, which thus provides a complete LQG of a Lorentzian gravity model in 3-dimensional space-time.

gr-qc↗

arXiv2012

Quantization of Lorentzian 3d Gravity by Partial Gauge Fixing

D = 2+1 gravity with a cosmological constant has been shown by Bonzom and Livine to present a Barbero-Immirzi like ambiguity depending on a parameter. We make use of this fact to show that, for positive cosmological constant, the Lorentzian theory can be partially gauge fixed and reduced to an SU(2) Chern-Simons theory. We then review the already known quantization of the latter in the framework of Loop Quantization for the case of space being topogically a cylinder. We finally construct, in the same setting, a quantum observable which, although non-trivial at the quantum level, corresponds to a null classical quantity.

gr-qc↗

arXiv2012

Loop Quantization of the Supersymmetric Two-Dimensional BF Model

In this paper we consider the quantization of the 2d BF model coupled to topological matter. Guided by the rigid supersymmetry this system can be viewed as a super-BF model, where the field content is expressed in terms of superfields. A canonical analysis is done and the constraints are then implemented at the quantum level in order to construct the Hilbert space of the theory under the perspective of Loop Quantum Gravity methods.

gr-qc↗

arXiv2010

Lorentz and CPT violation in QED revisited: A missing analysis

We investigate the breakdown of Lorentz symmetry in QED by a CPT violating interaction term consisting of the coupling of an axial fermion current with a constant vector field $b$, in the framework of algebraic renormalization -- a regularization-independent method. We show, to all orders in perturbation theory, that a CPT-odd and Lorentz violating Chern-Simons-like term, definitively, is not radiatively induced by the axial coupling of the fermions with the constant vector $b$.

hep-th↗

arXiv2010

The Hilbert space of Chern-Simons theory on the cylinder. A Loop Quantum Gravity approach

As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define at the quantum level the constraints appearing in the canonical approach and completely solve them, thus constructing a gauge and diffeomorphism invariant physical Hilbert space for the theory. This space turns out to be infinite dimensional, but separable.

gr-qc↗