General Solutions of Relativistic Wave Equations II: Arbitrary Spin Chains

A construction of relativistic wave equations on the homogeneous spaces of the Poincar\'{e} group is given for arbitrary spin chains. Parametrizations of the field functions and harmonic analysis on the homogeneous spaces are studied. It is shown that a direct product of Minkowski spacetime and two-dimensional complex sphere is the most suitable homogeneous space for the physical applications. The Lagrangian formalism and field equations on the Poincar\'{e} and Lorentz groups are considered. A boundary value problem for the relativistically invariant system is defined. General solutions of this problem are expressed via an expansion in hyperspherical functions defined on the complex two-sphere.Comment: 56 pages, LaTeX2

Classification of quantum relativistic orientable objects

Started from our work "Fields on the Poincare Group and Quantum Description of Orientable Objects" (EPJC,2009), we consider here a classification of orientable relativistic quantum objects in 3+1 dimensions. In such a classification, one uses a maximal set of 10 commuting operators (generators of left and right transformations) in the space of functions on the Poincare group. In addition to usual 6 quantum numbers related to external symmetries (given by left generators), there appear additional quantum numbers related to internal symmetries (given by right generators). We believe that the proposed approach can be useful for description of elementary spinning particles considering as orientable objects. In particular, their classification in the framework of the approach under consideration reproduces the usual classification but is more comprehensive. This allows one to give a group-theoretical interpretation to some facts of the existing phenomenological classification of known spinning particles.Comment: 24 page

Field on Poincare group and quantum description of orientable objects

We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner's ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with the help of two reference frames (space-fixed and body-fixed). A technical realization of this generalization (for instance, in 3+1 dimensions) amounts to introducing wave functions that depend on elements of the Poincare group $G$. A complete set of transformations that test the symmetries of an orientable object and of the embedding space belongs to the group $\Pi =G\times G$. All such transformations can be studied by considering a generalized regular representation of $G$ in the space of scalar functions on the group, $f(x,z)$, that depend on the Minkowski space points $x\in G/Spin(3,1)$ as well as on the orientation variables given by the elements $z$ of a matrix $Z\in Spin(3,1)$. In particular, the field $f(x,z)$ is a generating function of usual spin-tensor multicomponent fields. In the theory under consideration, there are four different types of spinors, and an orientable object is characterized by ten quantum numbers. We study the corresponding relativistic wave equations and their symmetry properties.Comment: 46 page

The Multivalued Free-Field Maps of Liouville and Toda Gravities

Liouville and Toda gravity theories with non-vanishing interaction potentials have spectra obtained by dividing the free-field spectra for these cases by the Weyl group of the corresponding $A_1$ or $A_2$ Lie algebra. We study the canonical transformations between interacting and free fields using the technique of intertwining operators, giving explicit constructions for the wavefunctions and showing that they are invariant under the corresponding Weyl groups. These explicit constructions also permit a detailed analysis of the operator-state maps and of the nature of the Seiberg bounds.Comment: 47 pages, plain Tex, 5 Postscript figures, uses epsf.tex. Repackaging to permit Postscript generation, no changes to pape

Quantization of fields over de Sitter space by the method of generalized coherent states

A system of generalized coherent states for the de Sitter group obeying the Klein-Gordon equation and corresponding to the massive spin zero particles over the de Sitter space is considered. This allows us to construct the quantized scalar field by the resolution over these coherent states; the corresponding propagator is computed by the method of analytic continuation to the complex de Sitter space and coincides with expressions obtained previously by other methods. Considering the case of spin 1/2 we establish the connection of the invariant Dirac equation over the de Sitter space with irreducible representations of the de Sitter group. The set of solutions of this equation is obtained in the form of the product of two different systems of generalized coherent states for the de Sitter group. Using these solutions the quantized Dirac field over de Sitter space is constructed and its propagator is found. It is a result of action of some de Sitter invariant spinor operator onto the spin zero propagator with an imaginary shift of a mass. We show that the constructed propagators possess the de Sitter-invariance and causality properties.Comment: 19 pages, LATEX, using ioplppt.sty and iopfts.st

Towards Relativistic Atomic Physics. I. The Rest-Frame Instant Form of Dynamics and a Canonical Transformation for a System of Charged Particles plus the Electro-Magnetic Field

A complete exposition of the rest-frame instant form of dynamics for arbitrary isolated systems (particles, fields, strings, fluids)admitting a Lagrangian description is given. The starting point is the parametrized Minkowski theory describing the system in arbitrary admissible non-inertial frames in Minkowski space-time, which allows one to define the energy-momentum tensor of the system and to show the independence of the description from the clock synchronization convention and from the choice of the 3-coordinates. In the inertial rest frame the isolated system is seen as a decoupled non-covariant canonical external center of mass carrying a pole-dipole structure (the invariant mass $M$ and the rest spin ${\vec {\bar S}}$ of the system) and an external realization of the Poincare' group. Then an isolated system of positive-energy charged scalar articles plus an arbitrary electro-magnetic field in the radiation gauge is investigated as a classical background for defining relativistic atomic physics. The electric charges of the particles are Grassmann-valued to regularize the self-energies. The rest-frame conditions and their gauge-fixings (needed for the elimination of the internal 3-center of mass) are explicitly given. It is shown that there is a canonical transformation which allows one to describe the isolated system as a set of Coulomb-dressed charged particles interacting through a Coulomb plus Darwin potential plus a free transverse radiation field: these two subsystems are not mutually interacting and are interconnected only by the rest-frame conditions and the elimination of the internal 3-center of mass. Therefore in this framework with a fixed number of particles there is a way out from the Haag theorem,at least at the classical level.Comment: Minor change

Therapy targeting antigen-specific T cells by a peptide-based tolerizing vaccine against autoimmune arthritis

A longstanding goal has been to find an antigen-specific preventive therapy, i.e., a vaccine, for autoimmune diseases. It has been difficult to find safe ways to steer the targeting of natural regulatory antigen. Here, we show that the administration of exogenous mouse major histocompatibility complex class II protein bounding a unique galactosylated collagen type II (COL2) peptide (Aq-galCOL2) directly interacts with the antigen-specific TCR through a positively charged tag. This leads to expanding a VISTA-positive nonconventional regulatory T cells, resulting in a potent dominant suppressive effect and protection against arthritis in mice. The therapeutic effect is dominant and tissue specific as the suppression can be transferred with regulatory T cells, which downregulate various autoimmune arthritis models including antibody-induced arthritis. Thus, the tolerogenic approach described here may be a promising dominant antigen-specific therapy for rheumatoid arthritis, and in principle, for autoimmune diseases in general.Knut and Alice Wallenberg Foundation (2019-0059)Swedish Research Council (2019-1209, 2017-06014)Swedish Association against RheumatismErling Persson Foundation (2017-10-09)German Federal Ministry of Education and Research (GO-Bio-project aidCURE; 031A385)Federal State of Hesse (LOEWE-project 13, IME Fraunhofer Project Group TMP at Goethe University)Fraunhofer Cluster of Excellence for Immune-Mediated Diseases CIMDSpanish Ministry of Universities through the European Union (NextGeneration EU)Publishe

Rapid T1 quantification based on 3D phase sensitive inversion recovery

<p>Abstract</p> <p>Background</p> <p>In Contrast Enhanced Magnetic Resonance Imaging fibrotic myocardium can be distinguished from healthy tissue using the difference in the longitudinal <it>T</it>₁relaxation after administration of Gadolinium, the so-called Late Gd Enhancement. The purpose of this work was to measure the myocardial absolute <it>T</it>₁post-Gd from a single breath-hold 3D Phase Sensitivity Inversion Recovery sequence (PSIR). Equations were derived to take the acquisition and saturation effects on the magnetization into account.</p> <p>Methods</p> <p>The accuracy of the method was investigated on phantoms and using simulations. The method was applied to a group of patients with suspected myocardial infarction where the absolute difference in relaxation of healthy and fibrotic myocardium was measured at about 15 minutes post-contrast. The evolution of the absolute <it>R</it>₁relaxation rate (1/<it>T</it>₁) over time after contrast injection was followed for one patient and compared to <it>T</it>₁mapping using Look-Locker. Based on the <it>T</it>₁maps synthetic LGE images were reconstructed and compared to the conventional LGE images.</p> <p>Results</p> <p>The fitting algorithm is robust against variation in acquisition flip angle, the inversion delay time and cardiac arrhythmia. The observed relaxation rate of the myocardium is 1.2 s^-1, increasing to 6 - 7 s^-1after contrast injection and decreasing to 2 - 2.5 s^-1for healthy myocardium and to 3.5 - 4 s^-1for fibrotic myocardium. Synthesized images based on the <it>T</it>₁maps correspond very well to actual LGE images.</p> <p>Conclusions</p> <p>The method provides a robust quantification of post-Gd <it>T</it>₁relaxation for a complete cardiac volume within a single breath-hold.</p

Anti-citrullinated protein antibodies cause arthritis by cross-reactivity to joint cartilage

Today, it is known that autoimmune diseases start a long time before clinical symptoms appear. Anti-citrullinated protein antibodies (ACPAs) appear many years before the clinical onset of rheumatoid arthritis (RA). However, it is still unclear if and how ACPAs are arthritogenic. To better understand the molecular basis of pathogenicity of ACPAs, we investigated autoantibodies reactive against the C1 epitope of collagen type II (CII) and its citrullinated variants. We found that these antibodies are commonly occurring in RA. A mAb (ACC1) against citrullinated C1 was found to cross-react with several noncitrullinated epitopes on native CII, causing proteoglycan depletion of cartilage and severe arthritis in mice. Structural studies by X-ray crystallography showed that such recognition is governed by a shared structural motif "RG-TG" within all the epitopes, including electrostatic potential-controlled citrulline specificity. Overall, we have demonstrated a molecular mechanism that explains how ACPAs trigger arthritis