Related papers: Single-valued integration and double copy

We introduce a new variant of Hochschild's two-sided bar construction for the setting of curved differential graded algebras. One can geometrically think of the classical bar complex as elements from the algebra positioned along different…

A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…

The period is a classical complex analytic invariant for a compact Riemann surface defined by integration of differential 1-forms. It has a strong relationship with the complex structure of the surface. In this chapter, we review another…

We present a new duality between the F-terms of supersymmetric field theories defined in two- and four-dimensions respectively. The duality relates N=2 supersymmetric gauge theories in four dimensions, deformed by an Omega-background in one…

This is the second installment of a series of papers aimed at developing a theory of Hrushovski-Kazhdan style motivic integration for certain types of nonarchimedean $o$-minimal fields, namely power-bounded $T$-convex valued fields, and…

In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semi-classical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex…

We study a family of generalized hypergeometric integrals defined on punctured Riemann surfaces of genus g. These integrals are closely related to g-loop string amplitudes in chiral splitting, where one leaves the loop-momenta, moduli and…

We propose a new approach that allows for the separate numerical calculation of the real and imaginary parts of finite loop integrals. We find that at one-loop the real part is given by the Loop-Tree Duality integral supplemented with…

We establish an Eichler-Shimura isomorphism for weakly modular forms of level one. We do this by relating weakly modular forms with rational Fourier coefficients to the algebraic de Rham cohomology of the modular curve with twisted…

Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher-order corrections by integration over linear statistics…

This article develops a novel approach to the representation of singular integral operators of Calder\'on-Zygmund type in terms of continuous model operators, in both the classical and the bi-parametric setting. The representation is…

We develop the notion of entwinement to characterize the amount of quantum entanglement between internal, discretely gauged degrees of freedom in a quantum field theory. This concept originated in the program of reconstructing spacetime…

We study in detail certain natural continuous representations of G = GL(n,K) in locally convex vector spaces over a locally compact, non-archimedean field K of characteristic zero. We construct boundary value maps, or integral transforms,…

An integration by parts formula is the foundation for stochastic analysis on path spaces over a (finite dimensional) Riemannian manifold or over $R^n$, from which we may deduce the operator $d$ is closable and define the Laplacian operator…

In this work, we investigate a theory of stochastic integration for operator-valued processes with respect to semimartingales taking values in the dual of a nuclear space. Our construction of this particular stochastic integral relies on…

The monodromy relations in string theory provide a powerful and elegant formalism to understand some of the deepest properties of tree-level field theory amplitudes, like the color-kinematics duality. This duality has been instrumental in…

Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…

It is known that the unified transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coefficient evolution equation on the finite interval or the half-line. In contrast, classical methods…

We discuss some applications of the Morse-Novikov theory to some problems in modern physics, where appears a non-exact closed 1-form $\omega$ (a multi-valued functional). We focus mainly our attention to the cohomology of the de Rham…

An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on R^d. As reference measures,…