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

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

Therapeutic vaccination of active arthritis with a glycosylated collagen type II peptide in complex with MHC class II molecules.

In both collagen-induced arthritis (CIA) and rheumatoid arthritis, T cells recognize a galactosylated peptide from type II collagen (CII). In this study, we demonstrate that the CII259-273 peptide, galactosylated at lysine 264, in complex with Aq molecules prevented development of CIA in mice and ameliorated chronic relapsing disease. In contrast, nonglycosylated CII259-273/Aq complexes had no such effect. CIA dependent on other MHC class II molecules (Ar/Er) was also down-regulated, indicating a bystander vaccination effect. T cells could transfer the amelioration of CIA, showing that the protection is an active process. Thus, a complex between MHC class II molecules and a posttranslationally modified peptide offers a new possibility for treatment of chronically active autoimmune inflammation such as rheumatoid arthritis