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Ludwig Streit

Publications and source records attributed to Ludwig Streit.

30 records · Page 2Linked to original sources
arXiv2008

Feynman integrals as Hida distributions: the case of non-perturbative potentials

Feynman integrands are constructed as Hida distributions. For our approach we first have to construct solutions to a corresponding Schroedinger equation with time-dependent potential. This is done by a generalization of the Doss approach to time-dependent potentials. This involves an expectation w.r.t. a complex scaled Brownian motion. As examples polynomial potentials of degree $4n+2, n\in\mathbb N,$ and singular potentials of the form $\frac{1}{|x|^n}, n\in\mathbb N$ and $\frac{1}{x^n}, n\in\mathbb N,$ are worked out.

math-ph↗
arXiv2008

Searching for Communities in Bipartite Networks

Bipartite networks are a useful tool for representing and investigating interaction networks. We consider methods for identifying communities in bipartite networks. Intuitive notions of network community groups are made explicit using Newman's modularity measure. A specialized version of the modularity, adapted to be appropriate for bipartite networks, is presented; a corresponding algorithm is described for identifying community groups through maximizing this measure. The algorithm is applied to networks derived from the EU Framework Programs on Research and Technological Development. Community groups identified are compared using information-theoretic methods.

physics.soc-ph↗
arXiv2004

Feynman integrals for non-smooth and rapidly growing potentials

The Feynman integral for the Schroedinger propagator is constructed as a generalized function of white noise, for a linear space of potentials spanned by measures and Laplace transforms of measures, i.e., locally singular as well as rapidly growing at infinity. Remarkably, all these propagators admit a perturbation expansion.

math-ph↗
arXiv2003

More About Donsker's Delta Function

We discuss Donsker's delta function within the framework of White Noise Analysis, in particular its extension to complex arguments. With a view towards applications to quantum physics we also study sums and products of Donsker's delta functions.

math-ph↗
arXiv2003

Quantum Mechanical Propagators in Terms of Hida Distributions

We review some basic notions and results of White Noise Analysis that are used in the construction of the Feynman integrand as a generalized White Noise functional. After sketching this construction for a large class of potentials we show that the resulting Feynman integrals solve the Schroedinger equation.

math-ph↗
arXiv2002

Generalized Functions in Infinite Dimensional Analysis

We give a general approach to infinite dimensional non-Gaussian Analysis for measures which need not have a logarithmic derivative. This framework also includes the possibility to handle measures of Poisson type.

math.FA↗
arXiv2002

A Note on Positive Distributions in Gaussian Analysis

We describe positive generalized functionals in Gaussian Analysis. We focus on distribution spaces larger than the space of Hida Distributions. It is shown that a positive distribution is represented by a measure with specific growth of its moments. Equivalently this may be replaced by an integrability condition.

math.FA↗
arXiv1999

Differential Geometry on Compound Poisson Space

In this paper we carry out analysis and geometry for a class of infinite dimensional manifolds, namely, compound configuration spaces as a natural generalization of the work \cite{AKR97}. More precisely a differential geometry is constructed on the compound configuration space $Ω_{X}$ over a Riemannian manifold $X$. This geometry is obtained as a natural lifting of the Riemannian structure on $X$. In particular, the intrinsic gradient, divergence, and Laplace-Beltrami operator are constructed. Therefore the corresponding Dirichlet forms on $L^{2}(Ω_{X})$ can be defined. Each is shown to be associated with a diffusion process on $Ω_{X}$ (so called equilibrium process) which is nothing but the diffusion process on the simple configuration space $Γ_{X}$ together with corresponding marks. As another consequence of our results we obtain a representation of the Lie-algebra of compactly supported vector fields on $X$ on compound Poisson space. Finally generalizations to the case when the compound Poisson measure is replaced by a marked Poisson measure easily follow from this construction.

math.FA↗
arXiv1999

Generalized Appell Systems

We give a general approach to infinite dimensional non-Gaussian analysis which generalizes the work \cite{KSWY95}. For given measure we construct a family of biorthogonal systems. We study their properties and their Gel'fand triples that they generate. As an example we consider the measures of Poisson type.

math.FA↗
arXiv1999

Analysis on Poisson and Gamma spaces

We study the spaces of Poisson, compound Poisson and Gamma noises as special cases of a general approach to non-Gaussian white noise calculus, see \cite{KSS96}. We use a known unitary isomorphism between Poisson and compound Poisson spaces in order to transport analytic structures from Poisson space to compound Poisson space. Finally we study a Fock type structure of chaos decomposition on Gamma space.

math.FA↗
arXiv1999

Knots, Feynman Diagrams and Matrix Models

An U(N)-invariant matrix model with d matrix variables is studied. It was shown that in the limit $N\to \infty $ and $d\to 0$ the model describes the knot diagrams. We realize the free partition function of the matrix model as the generalized expectation of a Hida distribution $Φ_{N,d}$. This enables us to give a mathematically rigorous meaning to the partition function with interaction. For the generalized function $Φ_{N,d}$ we prove a Wick theorem and we derive explicit formulas for the propagators.

math.QA↗