相关论文: Feynman-Jackson integrals

In the present review we provide an extensive analysis of the intertwinement between Feynman integrals and cohomology theories in the light of the recent developments. Feynman integrals enter in several perturbative methods for solving non…

We propose to call a class of deformed Feynman integrals as twisted Feynman integrals, where the integrand has an additional exponential factor linear in loop momenta. Such integrals appear in various contexts: tensor reduction of Feynman…

We find Feynman-Kac type representation theorems for generalized diffusions. To do this we need to establish existence, uniqueness and regularity results for equations with measure-valued coefficients.

A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. Integral representations, supporting the same class of…

In this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson's…

Feynman's path integral is generalized to quantum mechanics on p-adic space and time. Such p-adic path integral is analytically evaluated for quadratic Lagrangians. Obtained result has the same form as that one in ordinary quantum…

Parametric Feynman integrals with the regions of integration defined by some polynomials are considered in this paper. It is shown that integrals with irregular integration regions can be converted to standard parametric integrals, for…

We present the Feynman rules for leading-twist gauge-invariant quark and gluon operators with an arbitrary number of total derivatives and applicable to any order in perturbation theory. This generalizes previous results and constitutes a…

We discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method. We demonstrate the results for a class of two-point two-loop diagrams and the evaluation of most…

We give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The…

We discuss path integrals for quantum mechanics with a potential which is a perturbation of the upside-down oscillator. We express the path integral (in the real time) by the Wiener measure. We obtain the Feynman integral for perturbations…

We provide combinatorial as well as probabilistic interpretations for the q-analogue of the Pochhammer k-symbol introduced by Diaz and Teruel. We introduce q-analogues of the Mellin transform in order to study the q-analogue of the k-gamma…

We show that the Lee-Pomeransky parametric representation of Feynman integrals can be understood as a solution of a certain Gel'fand-Kapranov-Zelevinsky (GKZ) system. In order to define such GKZ system, we consider the polynomial obtained…

High precision calculations in perturbative QFT often require evaluation of big collection of Feynman integrals. Complexity of this task can be greatly reduced via the usage of linear identities among Feynman integrals. Based on…

In this paper, we introduce a new type of $ pq $-calculus. The $ pq $-derivative and $ pq $-integration are investigated and various properties of these concepts are given. The fundamental theorem of $ pq $-calculus and formulas of $ pq…

In perturbative calculations of quantum mechanical path integrals in curvilinear coordinates, Feynman diagrams involve multiple temporal integrals over products of distributions, which are mathematically undefined. We derive simple rules…

Dimensionally or analytically regulated Feynman integrals lead to relative twisted period integrals. We present a recent extension of the Griffiths-Dwork pole reduction algorithm for deriving the D-module of differential operators acting on…

In this paper we study an analytic Yeh--Feynman integral and an analytic Yeh--Fourier--Feynman transform associated with Gaussian processes. Fubini theorems involving the generalized analytic Yeh--Feynman integrals are established. The…

An automated treatment of iterated integrals based on letters induced by real-valued quadratic forms and Kummer--Poincar\'e letters is presented. These quantities emerge in analytic single and multi--scale Feynman diagram calculations. To…

A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In this letter we derive extremely compact…