79,233 research outputs found
Wick's Theorem for non-symmetric normal ordered products and contractions
We consider arbitrary splits of field operators into two parts, and use the
corresponding definition of normal ordering introduced by Evans and Steer. In
this case the normal ordered products and contractions have none of the special
symmetry properties assumed in existing proofs of Wick's theorem. Despite this,
we prove that Wick's theorem still holds in its usual form as long as the
contraction is a c-number. Wick's theorem is thus shown to be much more general
than existing derivations suggest, and we discuss possible simplifying
applications of this result.Comment: 17 page
Condensation transitions in a model for a directed network with weighted links
An exactly solvable model for the rewiring dynamics of weighted, directed
networks is introduced. Simulations indicate that the model exhibits two types
of condensation: (i) a phase in which, for each node, a finite fraction of its
total out-strength condenses onto a single link; (ii) a phase in which a finite
fraction of the total weight in the system is directed into a single node. A
virtue of the model is that its dynamics can be mapped onto those of a
zero-range process with many species of interacting particles -- an exactly
solvable model of particles hopping between the sites of a lattice. This
mapping, which is described in detail, guides the analysis of the steady state
of the network model and leads to theoretical predictions for the conditions
under which the different types of condensation may be observed. A further
advantage of the mapping is that, by exploiting what is known about exactly
solvable generalisations of the zero-range process, one can infer a number of
generalisations of the network model and dynamics which remain exactly
solvable.Comment: 23 pages, 8 figure
Foundations of the Unified Modeling Language.
Object-oriented analysis and design is an increasingly popular software development method. The Unified Modeling
Language (UML) has recently been proposed as a standard language for expressing object-oriented designs. Unfortunately, in its present form the UML lacks precisely defined semantics. This means that it is difficult to determine whether a design is consistent, whether a design modification is correct and whether a program correctly implements a design.
Formal methods provide the rigor which is lacking in object-oriented design notations. This provision is often
at the expense of clarity of exposition for the non-expert. Formal methods aim to use mathematical techniques in
order to allow software development activities to be precisely defined, checked and ultimately automated. This paper aims to present an overview of work being undertaken to provide (a sub-set of) the UML with formal semantics. The
semantics will facilitate the use of the UML in the software development process by allowing development steps to be defined and checked
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