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

Clinical validation of three cardiovascular magnetic resonance techniques to measure strain and torsion in patients with suspected coronary artery disease

BackgroundSeveral cardiovascular magnetic resonance (CMR) techniques can measure myocardial strain and torsion with high accuracy. The purpose of this study was to compare displacement encoding with stimulated echoes (DENSE), tagging and feature tracking (FT) for measuring circumferential and radial myocardial strain and myocardial torsion in order to assess myocardial function and infarct scar burden both at a global and at a segmental level. Method116 patients with a high likelihood of coronary artery disease (European SCORE &gt; 15%) underwent CMR examination including cine images, tagging, DENSE and late gadolinium enhancement (LGE) in the short axis direction. In total, 97 patients had signs of myocardial disease and 19 had no abnormalities in terms of left ventricular (LV) wall mass index, LV ejection fraction, wall motion, LGE or a history of myocardial infarction. Thirty-four patients had myocardial infarct scar with a transmural LGE extent (transmurality) that exceeded 50% of the wall thickness in at least one segment. Global circumferential strain (GCS) and global radial strain (GRS) was analyzed using FT of cine loops, deformation of tag lines or DENSE displacement. ResultsDENSE and tagging both showed high sensitivity (82% and 71%) at a specificity of 80% for the detection of segments with &gt; 50% LGE transmurality, and receiver operating characteristics (ROC) analysis showed significantly higher area under the curve-values (AUC) for DENSE (0.87) than for tagging (0.83, p &lt; 0.001) and FT (0.66, p = 0.003). GCS correlated with global LGE when determined with DENSE (r = 0.41), tagging (r = 0.37) and FT (r = 0.15). GRS had a low but significant negative correlation with LGE; DENSE r = − 0.10, FT r = − 0.07 and tagging r = − 0.16. Torsion from DENSE and tagging had a weak correlation (− 0.20 and − 0.22 respectively) with global LGE. ConclusionCircumferential strain from DENSE detected segments with &gt; 50% scar with a higher AUC than strain determined from tagging and FT at a segmental level. GCS and torsion computed from DENSE and tagging showed similar correlation with global scar size, while when computed from FT, the correlation was lower.Funding agencies: Linkoping University Library; EU FP 7European Union (EU) [223615]; Swedish Heart Lung FoundationSwedish Heart-Lung Foundation [20120449]; Swedish Research CouncilSwedish Research Council; Medical Research Council of Southeast Sweden [35141, 88731, 157921]</p