We describe methods for evaluating one-loop integrals in 4−2 dimensions. We give a recursion relation that expresses the scalar n-point integral as a cyclicly symmetric combination of (n− 1)point integrals. The computation of such integrals thus reduces to the calculation of box diagrams (n = 4). The tensor integrals required in gauge theory may be obtained by differentiating the scalar integra...

Imaginary-time correlation functions calculated by quantum Monte Carlo (QMC) are analyzed using the maximum entropy method (MaxEnt) to determine the ground-state energy and spectral overlap function. In contrast to earlier applications of MaxEnt, the data is obtained from importanced-sampled zero-temperature quantum Monte Carlo simulations. The analysis includes two steps. First, that spectral ...

6 It is the purpose of this short article to analyze mass conservation in high-order rigorous 7 remapping schemes, which contrary to flux-based methods, relies on elaborate integral con8 straints over overlap areas and reconstruction functions. For applications on the sphere these 9 integral constraints may be violated primarily due to inexact or ill-conditioned integration 10 and we propose a ...

An algorithm for the reduction of Feynman integrals with any number of loops and external momenta to a minimal set of basic integrals is proposed. The method is based on the new algorithms for evaluating tensor integrals, representation of generalized recurrence relations for a given kind of integrals as a linear system of PDEs and the reduction of this system to a standard form. Basic integral...

We consider integrals of type ∫ On u1 11 . . . u an 1nu b1 21 . . . u bn 2n du, with respect to the Haar measure on the orthogonal group. We establish several remarkable invariance properties satisfied by such integrals, by using combinatorial methods. We present as well a general formula for such integrals, as a sum of products of factorials. Introduction The computation of polynomial integral...

We consider an application involving a financial quadratic portfolio of options, when the joint underlying log-returns changes with multivariate elliptic distribution. This motivates the need for methods for the approximation of multiple integrals over hyperboloids. A transformation is used to reduce the hyperboloid integrals to a product of two radial integrals and two spherical surface integr...

we consider the number of zeros of the integral $i(h) = oint_{gamma_h} omega$ of real polynomial form $omega$ of degree not greater than $n$ over a family of vanishing cycles on curves $gamma_h:$ $y^2+3x^2-x^6=h$, where the integral is considered as a function of the parameter $h$. we prove that the number of zeros of $i(h)$, for $0 < h < 2$, is bounded above by $2[frac{n-1}{2}]+1$.

We report on high-order harmonic (HHG) two-source interferometry (TSI) in molecular gases. We used a 0-π phase plate to create two bright spots at the focus of a lens by converting a Gaussian laser beam into a TEM01 Transverse Electromagnetic Mode. The two bright foci produce two synchronized HHG sources. One of them is used to probe on-going dynamics in the generating medium, while the other s...