Related papers: The Feynman graph representation of convolution se…
We consider an SDE in R^m of the type dX(t)=a(X(t))dt+dU(t) with a L\'evy process U and study the problem for the distribution of a solution to be regular in various senses. We do not impose any specific conditions on the L\'evy measure of…
In this paper, we establish the convergence of Feynman graph integrals on closed real-analytic K\"ahler manifolds and uncover the structural mechanism underlying this convergence. The key insight is that, using Getzler's rescaling…
The explicit form for the characteristic function of a stable distribution on the line is derived analytically by solving the associated functional equation and applying theory of regular variation, without appeal to the general…
Feynman diagrams are the foremost tool in the perturbative study of quantum field theory. In gauge theories, the full potential of this tool is revealed when it is combined with the Slavanov-Taylor identities associated with the local gauge…
A new powerful method to calculate Feynman diagrams is proposed. It consists in setting up a Taylor series expansion in the external momenta squared (in general multivariable). The Taylor coefficients are obtained from the original diagram…
We consider a model for chaotic diffusion with amplification on graphs associated with piecewise-linear maps of the interval. We investigate the possibility of having power-law tails in the invariant measure by approximate solution of the…
A T-dualized selfdual inspired formulation of massive vector fields coupled to arbitrary matter is generated; subsequently its perturbative series modeling a spontaneously broken gauge theory is analyzed. The new Feynman rules and external…
We present python libraries for Feynman graphs manipulation. The key feature of these libraries is usage of generalization of graph representation offered by B. G. Nickel et al. In this approach graph is represented in some unique…
We study nonlinear elliptic equations for operators corresponding to non-stable L\'evy diffusions. We include a sum of fractional Laplacians of different orders. Such operators are infinitesimal generators of non-stable (i.e., non…
The L\'evy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable…
In this note we outline some novel connections between the following fields: 1) Convolution calculus on white noise spaces 2) Pseudo-differential operators and L\'evy processes on infinite dimensional spaces 3) Feynman graph representations…
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…
We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}^{\sigma,\mu}[\varphi(u)]=f \quad\quad\text{in}\quad\quad…
As for the spatially homogeneous Boltzmann equation of Maxwellian molecules with the fractional Fokker-Planck diffusion term, we consider the Cauchy problem for its Fourier-transformed version, which can be viewed as a kinetic model for the…
We perform a thorough analysis of the relationship between discrete and series representation path integral methods, which are the main numerical techniques used in connection with the Feynman-Kac formula. First, a new interpretation of the…
We consider an evolution equation with the regularized fractional derivative of an order $\alpha \in (0,1)$ with respect to the time variable, and a uniformly elliptic operator with variable coefficients acting in the spatial variables.…
We introduce a general algebraic setting for describing linear boundary problems in a symbolic computation context, with emphasis on the case of partial differential equations. The general setting is then applied to the Cauchy problem for…
In this expository article we review recent advances in our understanding of the combinatorial and algebraic structure of perturbation theory in terms of Feynman graphs, and Dyson-Schwinger equations. Starting from Lie and Hopf algebras of…
We investigate the stationary diffusion equation with a coefficient given by a (transformed) L\'evy random field. L\'evy random fields are constructed by smoothing L\'evy noise fields with kernels from the Mat\'ern class. We show that…
We develop a systematic theory of eventually positive semigroups of linear operators mainly on spaces of continuous functions. By eventually positive we mean that for every positive initial condition the solution to the corresponding Cauchy…