相关论文: An example of Feynman-Jackson integral

We recall the question of geometric integrators in the context of Poisson geometry, and explain their construction. These Poisson integrators are tested in some mechanical examples. Their properties are illustrated numerically and they are…

We study asymptotic expansions of Gaussian integrals of analytic functionals on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an asymptotic equality coupling the Gaussian integral and the trace of the composition of…

We derive a $q$-analogue of the matrix sixth Painlev\'e system via a connection-preserving deformation of a certain Fuchsian linear $q$-difference system. In specifying the linear $q$-difference system, we utilize the correspondence between…

A new approach to compute Feynman Integrals is presented. It relies on an integral representation of a given Feynman Integral in terms of simpler ones. Using this approach, we present, for the first time, results for a certain family of…

In this paper, we give p-adic q-integral representation for the Kim's q-Bernstein polynomials and we give some interesting formulae realted to Carlitz's q-Bernoulli numbers.

It is shown how strictly four-dimensional integration by parts combined with differential renormalization and its infrared analogue can be applied for calculation of Feynman diagrams.

The purpose of this paper is to define generalized twisted q-Bernoulli numbers by using p-adic q-integrals. Furthermore, we construct a q-analogue of the p-adic generalized twisted L-functions which interpolate generalized twisted…

Feynman integrals obey linear relations governed by intersection numbers, which act as scalar products between vector spaces. We present a general algorithm for constructing multivariate intersection numbers relevant to Feynman integrals,…

We provide an explicit expression for the first order $q$-difference system for the Jackson integral of symmetric Selberg type. The $q$-difference system gives a generalization of $q$-analog of contiguous relations for the Gauss…

Recently (see [1]) I has introduced an interesting the Euler-Barnes multiple zeta function. In this paper we construct the q-analogue of Euler-Barnes multiple zeta function which interpolates the q-analogue of Frobenius-Euler numbers of…

In this paper, we consider the Carlitz's type q-analogue of Changhee numbers and polynomials and we give some explicit formulae for these numbers and polynomials.

We propose a regular way to construct lattice versions of $W$-algebras, both for quantum and classical cases. In the classical case we write the algebra explicitly and derive the lattice analogue of Boussinesq equation from the Hamiltonian…

We introduce the tools of intersection theory to the study of Feynman integrals, which allows for a new way of projecting integrals onto a basis. In order to illustrate this technique, we consider the Baikov representation of maximal cuts…

The aim of the presented research is to give a rigorous mathematical approach to Feynman path integrals based on strong (pathwise) approximations based on simple random walks.

We consider $q$-analytic derivations of the $q$-Gauss summation formula for a $\, _2\phi _1$ that respect the symmetry in its upper parameters.

In this letter some properties of the Gauss decomposition of quantum group $GL_q(n)$ with application to q-bosonization are considered.

This paper is a continuation of our recent paper with the same title, arXiv:0806.1596v1 [math.NT], where a number of integral equalities involving integrals of the logarithm of the Riemann zeta-function were introduced and it was shown that…

We introduce four q-analogs of the double Laplace transform and prove some of their main properties. Next we show how they can be used to solve some q-functional equations and partial q-differential equations.

A continuous analog of Gauss-Newton method for solving nonlinear ill-posed problems is proposed. Its converegence is proved. A numerical example is presented to demonstrate efficiency of the propsed method.

A geometrical approach to the calculation of N-point Feynman diagrams is reviewed. It is shown that the geometrical splitting yields useful connections between Feynman integrals with different momenta and masses. It is demonstrated how…