Related papers: New Results For the Five Point Function
We consider a generalization of the Bauer maximum principle. We work with tensorial products of convex measures sets, that are non necessarily compact but generated by their extreme points. We show that the maximum of a quasi-convex lower…
Collisions at the LHC produce many-particle final states, and for precise predictions the one-loop $N$-point corrections are needed. We study here the tensor reduction for Feynman integrals with $N \ge 6$. A general, recursive solution by…
In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…
A next-to-leading order calculation for single top production including spin-dependent observables requires efficient techniques for the calculation of the relevant loop amplitudes. We discuss the adaption of dimensional regularization, the…
Using the results recently obtained for computing integrals over (non-minimal) pure spinor superspace, we compute the coefficient of the massless two-loop four-point amplitude from first principles. Contrasting with the mathematical…
The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the…
Numerical interpolation techniques are widely employed for calculating large rational functions in scattering amplitude computations. It has been observed in recent years that these rational functions greatly simplify upon partial…
A useful identity relating the infinite sum of two Bessel functions to their infinite integral was discovered in Dominici et al. (2012). Here, we extend this result to products of $N$ Bessel functions, and show it can be straightforwardly…
We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as…
We reduce the computation of three point function of three spinning operators with arbitrary polarizations to a statistical mechanics problem via the hexagon formalism. The central building block of these correlation functions is the…
We propose novel smooth approximations to the classical rounding function, suitable for differentiable optimization and machine learning applications. Our constructions are based on two approaches: (1) localized sigmoid window functions…
The core of this article is a general theorem with a large number of specializations. Given a manifold $N$ and a finite number of one-parameter groups of point transformations on $N$ with generators $Y, X_{(1)}, \cdots, X_{(d)} $, we…
The fine structures on the $S$-spectrum constitute a new research area that includes a class of functional calculi based on the $S$-spectrum and on integral transforms determined by the Fueter--Sce mapping theorem and the Cauchy formula for…
In two remarkable recent papers, hep-th/0610248 and hep-th/0610251, the complete planar perturbative expansion was proposed for the universal function of the coupling, f(g), appearing in the dimensions of high-spin operators of the N=4 SYM…
We evaluate closed string disk amplitudes in the pure spinor formalism. We focus on low point functions (two- and one-point functions) but our analysis is also relevant for higher n-point functions. Amongst others we discuss issues arising…
For two integers $a$ and $b$, the plum-blossom product of $a$ and $b$ is defined as the ones of the usual product of $a$ and $b$ if the ones is less than or equal to $3$, or otherwise as the ones minus $10$. Under this operation, all…
We derive novel sufficient conditions for convergence of Loopy Belief Propagation (also known as the Sum-Product algorithm) to a unique fixed point. Our results improve upon previously known conditions. For binary variables with…
To avoid problems with infinite measure, the functional integral for harmonic oscillator can be calculated by time - slicing method with continuum limit procedure proposed Gelfand and Yaglom. In previous article we proved by nonperturbative…
We construct a new operation among representations of the symmetric group that interpolates between the classical internal and external products, which are defined in terms of tensor product and induction of representations. Following…
This paper introduces an efficient tensor-vector product technique for the rapid and accurate approximation of integral operators within physics-informed deep learning frameworks. Our approach leverages neural network architectures to…