181 research outputs found
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 . A
complete set of transformations that test the symmetries of an orientable
object and of the embedding space belongs to the group . All
such transformations can be studied by considering a generalized regular
representation of in the space of scalar functions on the group, ,
that depend on the Minkowski space points as well as on the
orientation variables given by the elements of a matrix .
In particular, the field 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 or 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 and the rest spin 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><sub>1 </sub>relaxation after administration of Gadolinium, the so-called Late Gd Enhancement. The purpose of this work was to measure the myocardial absolute <it>T</it><sub>1 </sub>post-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><sub>1 </sub>relaxation rate (1/<it>T</it><sub>1</sub>) over time after contrast injection was followed for one patient and compared to <it>T</it><sub>1 </sub>mapping using Look-Locker. Based on the <it>T</it><sub>1 </sub>maps 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<sup>-1</sup>, increasing to 6 - 7 s<sup>-1 </sup>after contrast injection and decreasing to 2 - 2.5 s<sup>-1 </sup>for healthy myocardium and to 3.5 - 4 s<sup>-1 </sup>for fibrotic myocardium. Synthesized images based on the <it>T</it><sub>1 </sub>maps correspond very well to actual LGE images.</p> <p>Conclusions</p> <p>The method provides a robust quantification of post-Gd <it>T</it><sub>1 </sub>relaxation 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
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