604 research outputs found
A new diagrammatic representation for correlation functions in the in-in formalism
In this paper we provide an alternative method to compute correlation
functions in the in-in formalism, with a modified set of Feynman rules to
compute loop corrections. The diagrammatic expansion is based on an iterative
solution of the equation of motion for the quantum operators with only retarded
propagators, which makes each diagram intrinsically local (whereas in the
standard case locality is the result of several cancellations) and endowed with
a straightforward physical interpretation. While the final result is strictly
equivalent, as a bonus the formulation presented here also contains less graphs
than other diagrammatic approaches to in-in correlation functions. Our method
is particularly suitable for applications to cosmology.Comment: 14 pages, matches the published version. includes a modified version
of axodraw.sty that works with the Revtex4 clas
Statistical ensemble of scale-free random graphs
A thorough discussion of the statistical ensemble of scale-free connected
random tree graphs is presented. Methods borrowed from field theory are used to
define the ensemble and to study analytically its properties. The ensemble is
characterized by two global parameters, the fractal and the spectral
dimensions, which are explicitly calculated. It is discussed in detail how the
geometry of the graphs varies when the weights of the nodes are modified. The
stability of the scale-free regime is also considered: when it breaks down,
either a scale is spontaneously generated or else, a "singular" node appears
and the graphs become crumpled. A new computer algorithm to generate these
random graphs is proposed. Possible generalizations are also discussed. In
particular, more general ensembles are defined along the same lines and the
computer algorithm is extended to arbitrary (degenerate) scale-free random
graphs.Comment: 10 pages, 6 eps figures, 2-column revtex format, minor correction
Generalized bent Boolean functions and strongly regular Cayley graphs
In this paper we define the (edge-weighted) Cayley graph associated to a
generalized Boolean function, introduce a notion of strong regularity and give
several of its properties. We show some connections between this concept and
generalized bent functions (gbent), that is, functions with flat Walsh-Hadamard
spectrum. In particular, we find a complete characterization of quartic gbent
functions in terms of the strong regularity of their associated Cayley graph.Comment: 13 pages, 2 figure
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