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Interacting Components
SystemCSP is a graphical modeling language based on both CSP and concepts of component-based software development. The component framework of SystemCSP enables specification of both interaction scenarios and relative execution ordering among components. Specification and implementation of interaction among participating components is formalized via the notion of interaction contract. The used approach enables incremental design of execution diagrams by adding restrictions in different interaction diagrams throughout the process of system design. In this way all different diagrams are related into a single formally verifiable system. The concept of reusable formally verifiable interaction contracts is illustrated by designing set of design patterns for typical fault tolerance interaction scenarios
A Table of Third and Fourth Order Feynman Diagrams of the Interacting Fermion Green's Function
The Feynman diagrams of the Green's function expansion of fermions
interacting with a non-relativistic 2-body interaction are displayed in first,
second and third order of the interaction as 2, 10 and 74 diagrams,
respectively. A name convention for the diagrams is proposed and then used to
tabulate the 706 diagrams of fourth order. The Hartree-Fock approximation
summons up 2, 8, 40 and 224 of them, respectively.Comment: 12 pages, 13 figures, 16 tables. Index typo in Sect III corrected.
More lines in Table XV. Three more references. Expanded Summar
Recursion Relation for the Feynman Diagrams of the Effective Action for the Third Legendre Transformation
We derive a recursion relation of the Feynman diagrams of the effective
action for the third Legendre transformation in case of the bosonic field
theory with cubic interaction. We apply the recursion relation to obtain the
Feynman diagrams of the effective action for the third Legendre transformation
up to the five-loop order. The three-particle irreducibility of the Feynman
diagrams of the effective action for the third Legendre transformation is shown
by induction
On Large Limit of Symmetric Traceless Tensor Models
For some theories where the degrees of freedom are tensors of rank or
higher, there exist solvable large limits dominated by the melonic
diagrams. Simple examples are provided by models containing one rank- tensor
in the tri-fundamental representation of the symmetry group. When the
quartic interaction is assumed to have a special tetrahedral index structure,
the coupling constant must be scaled as in the melonic large
limit. In this paper we consider the combinatorics of a large theory of one
fully symmetric and traceless rank- tensor with the tetrahedral quartic
interaction; this model has a single symmetry group. We explicitly
calculate all the vacuum diagrams up to order , as well as some diagrams
of higher order, and find that in the large limit where is held
fixed only the melonic diagrams survive. While some non-melonic diagrams are
enhanced in the symmetric theory compared to the one, we have
not found any diagrams where this enhancement is strong enough to make them
comparable with the melonic ones. Motivated by these results, we conjecture
that the model of a real rank- symmetric traceless tensor possesses a smooth
large limit where is held fixed and all the contributing diagrams
are melonic. A feature of the symmetric traceless tensor models is that some
vacuum diagrams containing odd numbers of vertices are suppressed only by
relative to the melonic graphs.Comment: 18 pages, 12 figures; v2: minor improvements, references adde
Diagrammatic theory of the Anderson impurity model with finite Coulomb interaction
We have developed a self-consistent conserving pseudo particle approximation
for the Anderson impurity model with finite Coulomb interaction, derivable from
a Luttinger Ward functional. It contains an infinite series of skeleton
diagrams built out of fully renormalized Green's functions. The choice of
diagrams is motivated by the Schrieffer Wolff transformation which shows that
singly and doubly occupied states should appear in all bare diagrams
symmetrically. Our numerical results for are in excellent agreement with
the exact values known from the Bethe ansatz solution. The low energy physics
of non-Fermi liquid Anderson impurity systems is correctly described while the
present approximation fails to describe Fermi liquid systems, since some
important coherent spin flip and charge transfer processes are not yet
included. It is believed that CTMA (Conserving T-matrix approximation) diagrams
will recover also Fermi liquid behavior for Anderson models with finite Coulomb
interaction as they do for infinite Coulomb interaction.Comment: 4 pages, 2 figures, presented at the NATO Advanced Research Workshop
on "Size Dependent MAgnetic Scattering", Pecs, Hungary, May 28 - June 1, 200
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