Soliton fermionic number from the heat kernel expansion

Producción CientíficaWe consider different methods of calculating the (fractional) fermion number of solitons based on the heat kernel expansion. We derive a formula for the localized η function that provides a more systematic version of the derivative expansion for spectral asymmetry and compute the fermion number in amulti flavor extension of the Goldstone–Wilczek model. We also propose an improved expansion of the heat kernel that allows the tackling of the convergence issues and permits an automated computation of the coefficients.Juant de Castilla y León grant BU 229P18

Edge states and the η\eta invariant

We propose a relation between the $\eta$ invariant on a manifold with boundary, the $\eta$ invariants of edge states, and the $\eta$ invariant in an infinite volume limit. With the example of planar fermions with bag and chiral bag boundary conditions we show that this relation holds whenever edge states are sufficiently well-localized near the boundary. As a by-product we show that the spectrum of edge modes for chiral bag boundary conditions is linear but bounded.Comment: 8 page

Non-topological fractional fermion number in the Jackiw-Rossi model

We compute the vacuum fermion current in $(2+1)$ dimensional Jackiw-Rossi model by using the $1/m$ expansion. The current is expressed through a weighted $\eta$-function with a matrix weight. In the presence of such a weight, the usual proof of topological nature of $\eta(0)$ is not longer applicable. Direct computations confirm the following surprising result: the fermion number induced by vortices in the Jackiw-Rossi model is \textit{not} topological.Comment: 8 pages, revte

Minimally invasive system to reliably characterize ventricular electrophysiology from living donors

Cardiac tissue slices preserve the heterogeneous structure and multicellularity of the myocardium and allow its functional characterization. However, access to human ventricular samples is scarce. We aim to demonstrate that slices from small transmural core biopsies collected from living donors during routine cardiac surgery preserve structural and functional properties of larger myocardial specimens, allowing accurate electrophysiological characterization. In pigs, we compared left ventricular transmural core biopsies with transmural tissue blocks from the same ventricular region. In humans, we analyzed transmural biopsies and papillary muscles from living donors. All tissues were vibratomesliced. By histological analysis of the transmural biopsies, we showed that tissue architecture and cellular organization were preserved. Enzymatic and vital staining methods verifed viability. Optically mapped transmembrane potentials confrmed that action potential duration and morphology were similar in pig biopsies and tissue blocks. Action potential morphology and duration in human biopsies and papillary muscles agreed with published ranges. In both pigs and humans, responses to increasing pacing frequencies and β-adrenergic stimulation were similar in transmural biopsies and larger tissues. We show that it is possible to successfully collect and characterize tissue slices from human myocardial biopsies routinely extracted from living donors, whose behavior mimics that of larger myocardial preparations both structurally and electrophysiologically.Fil: Oliván Viguera, Aida. Universidad de Zaragoza; EspañaFil: Pérez Zabalza, María. Universidad de Zaragoza; EspañaFil: García Mendívil, Laura. Universidad de Zaragoza; EspañaFil: Mountris, Konstantinos A.. Universidad de Zaragoza; EspañaFil: Orós Rodrigo, Sofía. Universidad de Zaragoza; EspañaFil: Ramos Marquès, Estel. Universidad de Zaragoza; EspañaFil: Vallejo Gil, José María. University Hospital Miguel Servet; EspañaFil: Fresneda Roldán, Pedro Carlos. University Hospital Miguel Servet; EspañaFil: Fañanás Mastral, Javier. University Hospital Miguel Servet; EspañaFil: Vázquez Sancho, Manuel. University Hospital Miguel Servet; EspañaFil: Matamala Adell, Marta. University Hospital Miguel Servet; EspañaFil: Sorribas Berjón, Fernando. University Hospital Miguel Servet; EspañaFil: Bellido Morales, Javier André. University Hospital Miguel Servet; EspañaFil: Mancebón Sierra, Francisco Javier. University Hospital Miguel Servet; EspañaFil: Vaca Núñez, Alexánder Sebastián. University Hospital Miguel Servet; EspañaFil: Ballester Cuenca, Carlos. University Hospital Miguel Servet; EspañaFil: Marigil, Miguel Ángel. Hospital San Jorge; EspañaFil: Pastor, Cristina. Aragón Institute of Health Sciences; EspañaFil: Ordovás, Laura. Aragón Agency for Research and Development; España. Universidad de Zaragoza; EspañaFil: Köhler, Ralf. Aragón Institute of Health Sciences; España. Aragón Agency for Research and Development; EspañaFil: Diez, Emiliano Raúl. Universidad Nacional de Cuyo. Facultad de Ciencias Médicas. Cátedra de Fisiología Humana Normal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto de Medicina y Biología Experimental de Cuyo; ArgentinaFil: Pueyo, Esther. Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina; España. Universidad de Zaragoza; Españ

Some quartization problems in theories with non-Abelian backgrounds and in non-commutative spacetimes

Esta tese tem por base três artigos publicados pelo autor e colaboradores. O primeiro artigo trata do problema da quantização de modelos pseudoclássicos de partículas escalares em campos de fundo não-abelianos, cujo foco é a dedução desses modelos pseudo-clássicos usando métodos de integral de trajetória. O segundo artigo investiga a possibilidade de realizar modelos de gravitação dilatônica em variedades não-comutativas em duas dimensões. Para tanto, vale-se de um método de análise de vínculos e simetrias especialmente desenvolvido para gravitação não-comutativa em duas dimensões. O terceiro artigo discute modelos renormalizáveis em espaços-tempo não-comutativos com parâmetro de não-comutatividade bifermiônico em quatro dimensões.This thesis is based on three published papers by the author and co-authors. The rst article treats the quantization problem of pseudoclassical models of scalar particles in non-Abelian backgrounds, which aims at deriving these models using path-integral methods. The second article examines the possibility of realizing dilaton gravity models in noncommutative two-dimensional manifolds. It relies upon a method of analysis of constraints and symmetries especially developed for non-commutative dilaton gravities in two dimensions. The third article discusses renormalizable models in noncommutative spacetime with bifermionic noncommutative parameter in four dimensions

Quantization of spinorial relativistic particle in 2+1 dimensions

Neste trabalho é considerado o problema da quantização de um modelo pseudoclássico para uma partícula relativística massiva de spin 1/2 em 2+1 dimensões em campos externos eletromagnéticos arbitrários. A quantização apresentada é uma combinação dos esquemas de quantização de Dirac e canônico, uma vez que o modelo aontém um vínculo ded primeira classe que não pode ser fixado por uma escolha de calibre. A presença deste vínculo no nível quântico leva a uma extensão do número de componentes dos vetores de estado em comparação com a teoria em 3+1 dimensões. A mecânica construída deescreve partículas e antipartículas ded energia positiva, em acordo com a teoria quântica de campos.We consider the quantization problem for a pseudoclassical model of a massive spin-1/2 relativistic particle in 2+1 dimensions on the backgroundof an arbitrary electromagnetic field. The presented quantization is a combination of the canonical and Dirac Schemes, since the model contains a first-class constraint which does not admit gauge-fixing. The presence of this constraint at the quantum level leads to an extension of the number of state-vector components in comparison with the 3+1 case. The constructed quantum mechanics describes both particles and antiparticles with positive energy levels, in accordance with quantum field theory

Edge states and the η invariant

We propose a relation between the η invariant on a manifold with boundary, the η invariants of edge states, and the η invariant in an infinite volume limit. With the example of planar fermions with bag and chiral bag boundary conditions we show that this relation holds whenever edge states are sufficiently well-localized near the boundary. As a by-product we show that the spectrum of edge modes for chiral bag boundary conditions is linear but bounded

Quantum localisation on the circle

International audienceCovariant integral quantisation using coherent states for semi-direct product groups is implemented for the motion of a particle on the circle. In this case, the phase space is the cylinder, which is viewed as a left coset of the Euclidean group E(2). Coherent states issued from fiducial vectors are labeled by points in the cylinder and depend also on extra parameters. We carry out the corresponding quantisations of the basic classical observables, particularly the angular momentum and the 2π-periodic discontinuous angle function. We compute their corresponding lower symbols. The quantum localisation on the circle is examined through the properties of the angle operator yielded by our procedure, its spectrum and lower symbol, its commutator with the quantum angular momentum, and the resulting Heisenberg inequality. Comparison with other approaches to the long-standing question of the quantum angle is discussed

Minimally invasive system to reliably characterize ventricular electrophysiology from living donors

Cardiac tissue slices preserve the heterogeneous structure and multicellularity of the myocardium and allow its functional characterization. However, access to human ventricular samples is scarce. We aim to demonstrate that slices from small transmural core biopsies collected from living donors during routine cardiac surgery preserve structural and functional properties of larger myocardial specimens, allowing accurate electrophysiological characterization. In pigs, we compared left ventricular transmural core biopsies with transmural tissue blocks from the same ventricular region. In humans, we analyzed transmural biopsies and papillary muscles from living donors. All tissues were vibratome-sliced. By histological analysis of the transmural biopsies, we showed that tissue architecture and cellular organization were preserved. Enzymatic and vital staining methods verified viability. Optically mapped transmembrane potentials confirmed that action potential duration and morphology were similar in pig biopsies and tissue blocks. Action potential morphology and duration in human biopsies and papillary muscles agreed with published ranges. In both pigs and humans, responses to increasing pacing frequencies and ß-adrenergic stimulation were similar in transmural biopsies and larger tissues. We show that it is possible to successfully collect and characterize tissue slices from human myocardial biopsies routinely extracted from living donors, whose behavior mimics that of larger myocardial preparations both structurally and electrophysiologically