2,624 research outputs found
On an easy transition from operator dynamics to generating functionals by Clifford algebras
Clifford geometric algebras of multivectors are treated in detail. These
algebras are build over a graded space and exhibit a grading or multivector
structure. The careful study of the endomorphisms of this space makes it clear,
that opposite Clifford algebras have to be used also. Based on this
mathematics, we give a fully Clifford algebraic account on generating
functionals, which is thereby geometric. The field operators are shown to be
Clifford and opposite Clifford maps. This picture relying on geometry does not
need positivity in principle. Furthermore, we propose a transition from
operator dynamics to corresponding generating functionals, which is based on
the algebraic techniques. As a calculational benefit, this transition is
considerable short compared to standard ones. The transition is not injective
(unique) and depends additionally on the choice of an ordering. We obtain a
direct and constructive connection between orderings and the explicit form of
the functional Hamiltonian. These orderings depend on the propagator of the
theory and thus on the ground state. This is invisible in path integral
formulations. The method is demonstrated within two examples, a non-linear
spinor field theory and spinor QED. Antisymmetrized and normal-ordered
functional equations are derived in both cases.Comment: 23p., 76kB, plain LaTeX, [email protected]
Mixed Symmetry Solutions of Generalized Three-Particle Bargmann-Wigner Equations in the Strong-Coupling Limit
Starting from a nonlinear isospinor-spinor field equation, generalized
three-particle Bargmann-Wigner equations are derived. In the strong-coupling
limit, a special class of spin 1/2 bound-states are calculated. These solutions
which are antisymmetric with respect to all indices, have mixed symmetries in
isospin-superspin space and in spin orbit space. As a consequence of this mixed
symmetry, we get three solution manifolds. In appendix \ref{b}, table 2, these
solution manifolds are interpreted as the three generations of leptons and
quarks. This interpretation will be justified in a forthcoming paper.Comment: 17 page
Statistical analysis of network data and evolution on GPUs: High-performance statistical computing
Network analysis typically involves as set of repetitive tasks that are particularly amenable to poor-man's parallelization. This is therefore an ideal application are for GPU architectures, which help to alleviate the tedium inherent to statistically sound analysis of network data. Here we will illustrate the use of GPUs in a range of applications, which include percolation processes on networks, the evolution of protein-protein interaction networks, and the fusion of different types of biomedical and disease data in the context of molecular interaction networks. We will pay particular attention to the numerical performance of different routines that are frequently invoked in network analysis problems. We conclude with a review over recent developments in the generation of random numbers that address the specific requirements posed by GPUs and high-performance computing needs
Surface circulation in the Great Lakes as observed by LANDSAT-1 August 1972 - December 1973: Southern Lake Michigan
The surface current circulation patterns of southern Lake Michigan were charted for all cardinal and subcardinal wind directions, employing LANDSAT-1 observations of the distribution of natural tracing material borne in the surface waters. These colorants consist chiefly of river discharges composed of suspended sediments, pollutants, and algae; extensive chemical precipitations proved valuable for areas farther from shore. Comparison of the satellite-derived surface current charts with previous theoretical and empirical studies shows good agreement
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