Nucleon spin decomposition and differential geometry

In the last few years, the so-called Chen et al. approach of the nucleon spin decomposition has been widely discussed and elaborated on. In this letter we propose a genuine differential geometric understanding of this approach. We mainly highligth its relation to the "dressing field method" we advocated in [C. Fournel, J. Fran\c{c}ois, S. Lazzarini, T. Masson, Int. J. Geom. Methods Mod. Phys. 11, 1450016 (2014)]. We are led to the conclusion that the claimed gauge-invariance of the Chen et al. decomposition is actually unreal.Comment: 9 pages. v3: minor corrections in the text, addition of a new referenc

Gauge field theories: various mathematical approaches

This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe Yang-Mills-Higgs theories or gravitation theories, and each of them improves the paradigm of gauge field theories. A brief comparison between them is carried out, essentially due to the various notions of connection. However they reveal a compelling common mathematical pattern on which the paper concludes.Comment: 33 pages. To be published in the book: Mathematical Structures of the Universe (Copernicus Center Press, Krak\'ow, Poland, 2014

Cartan Connections and Atiyah Lie Algebroids

This work extends previous developments carried out by some of the authors on Ehresmann connections on Atiyah Lie algebroids. In this paper, we study Cartan connections in a framework relying on two Atiyah Lie algebroids based on a $H$-principal fiber bundle $\mathcal{P}$ and its associated $G$-principal fiber bundle $\mathcal{Q} := \mathcal{P} \times_H G$, where $H \subset G$ defines the model for a Cartan geometry. The first main result of this study is a commutative and exact diagram relating these two Atiyah Lie algebroids, which allows to completely characterize Cartan connections on $\mathcal{P}$. Furthermore, in the context of gravity and mixed anomalies, our construction answers a long standing mathematical question about the correct geometrico-algebraic setting in which to combine inner gauge transformations and infinitesimal diffeomorphisms.Comment: 27 pages. Published versio

Twisted Gauge Fields

We propose a generalisation of the notion of associated bundles to a principal bundle constructed via group action cocycles rather than via mere representations of the structure group. We devise a notion of connection generalising Ehresmann connection on principal bundles, giving rise to the appropriate covariant derivative on sections of these twisted associated bundles (and on twisted tensorial forms). We study the action of the group of vertical automorphisms on the objects introduced (active gauge transformations). We also provide the gluing properties of the local representatives (passive gauge transformations). The latter are generalised gauge fields: They satisfy the gauge principle of physics, but are of a different geometric nature than standard Yang-Mills fields. We also examine the conditions under which this new geometry coexists and mixes with the standard one. We show that (standard) conformal tractors and Penrose's twistors can be seen as simple instances of this general picture. We also indicate that the twisted geometry arises naturally in the definition and study of anomalies in quantum gauge field theory.Comment: 33 page

Artificial vs Substantial Gauge Symmetries: a Criterion and an Application to the Electroweak Model

To systematically answer the generalized Kretschmann objection, we propose a mean to make operational a criterion widely recognized as allowing to decide if the gauge symmetry of a theory is artificial or substantial. Our proposition is based on the dressing field method of gauge symmetry reduction, a new simple tool from mathematical physics. This general scheme allows in particular to straightforwardly argue that the notion of spontaneous symmetry breaking is superfluous to the empirical success of the electroweak theory. Important questions regarding the context of justification of the theory then arise.Comment: 13 pages. Revised version accepted for publication in Philosophy of Science. The author thanks the two anonymous reviewers for their valuable inpu

Nonlinear jet-flap interactions: a dynamical-systems analysis

International audienceWe analyze the temporal dynamics associated with the jet-flap interactions by carrying-out a dynamical-systems analysis. The experimental cases are characterized by three different setups of the jet-flap system, running in the range M a = 0.6 − 1.0. The analysis is based on data presented by Jordan et al., 1 where the self-sustained oscillations were analyzed by means of linear models. Nonlinear competition among the modes was observed: here we analyze this interplay by investigating the system using statistical tools, phase portraits, Poincaré sections, and return maps. We estimate the minimal number of degrees of freedom necessary for the description of a nonlinear model. The correlation dimension is assessed for four representative cases. Finally, we analyze the toroidal geometry in the phase-space and identify the main ingredients necessary for nonlinear reduced-order models of this system

Étude théorique de la transition de phase a<->g du cérium (prise en compte des fortes corrélations en DFT+DMFT)

La transition de phase isostructurale du cérium a été et reste l'objet de nombreuses études pour tester les méthodes permettant de décrire les matériaux fortement corrélés.La Théorie du Champ Moyen Dynamique (DMFT) jointe à la Théorie de la fonctionnelle de la densité à permis de décrire de tels systèmes.Pourtant, le calcul des propriétés de l'état fondamental nécessite une très bonne précision de calcul à la fois de la part de la DFT et de la DMFT.Nous utilisons un résolveur Monte Carlo Quantique en Temps Continu (CT-QMC), rapide et capable de simuler les basses températures, combiné à une implantation ondes planes augmentées par projection de la DMFT pour calculer les énergies internes et libres - et par conséquent l'entropie - au cours de la transition de phase du cérium.D'importants calculs, utilisant cette implantation, nous ont permis de reconsidérer les propriétés de l'état fondamental et une grande partie de la thermodynamique de la transition de phase ag du cérium à basses températures.En particulier, le bruit stochastique est suffisamment faible pour interpréter, sans ambiguïté, les courbes énergie en fonction du volume.Sur ces dernières, un double point d'inflexion est clairement visible pour l'énergie interne jusqu'à une température relativement basse.Les courbes d'énergie libre mettent, de plus, en évidence l'importance de l'entropie pour ce système.D'autre part, les spectres de photoemission tout au long de la transition de phase sont analysés.Le schéma DMFT est comparé avec des calculs DFT récents et des données expérimentales récentes.Enfin, nous mettons en avant les approximations utilisées et nous nous interrogeons sur leurs validité.The isostructural phase transition of cerium has been and remains the aim of many studies in order to test methods developed to describe strongly correlated materials.The Dynamical Mean Field Theory (DMFT) combined with density functional theory (DFT) has been successful to describe such systems.However, the computation of the ground state properties requires a very good accuracy from both DFT and DMFT sides.We use thus a strong coupling Continuous Time Quantum Monte Carlo (CT-QMC) solver, which is fast and able to reach low temperatures, in combination with a projector augmented wave (PAW) DMFT implementation to calculate internls and free energies - and thus the entropy - during the phase transition of cerium.Extensive calculations using this implementation allows us to carefully reassess the ground state properties and almost all thermodynamics of the ag phase transition in cerium at low temperatures.In particular, stochastic noise is small enough to avoid any ambiguity on the interpretation of energy versus volume curves.On those curves, a double inflexion point is clearly observable ont the internal energy curves untill a relatively low temperature.Moreover, free energy curves highlight the importance of including the entropy contribution.The DMFT picture is put in perspective with recent DFT calculations and recent experimental investigations.Furthermore, photoemission spectra are analysed while the phase transition.Finaly, we discuss the approximations used and raise curiosity about their consideration.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF