Related papers: Quadratic Feynman Loop Integrands From Massless Sc…
Quantum Hamiltonians containing nonseparable products of non-commuting operators, such as $\hat{\bf x}^m \hat{\bf p}^n$, are problematic for numerical studies using split-operator techniques since such products cannot be represented as a…
Building on the prior work in [1] we locate a family of positive geometries in the kinematic space which are a specific class of convex realisations of the associahedron. These realisations are obtained by scaling and translating the…
We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the $\rho$-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be…
The Fueter-Sce-Qian mapping theorem is a two steps procedure to extend holomorphic functions of one complex variable to quaternionic or Clifford algebra-valued functions in the kernel of a suitable generalized Cauchy-Riemann operator. Using…
In order to generalize the integration rules to general CHY integrands which include higher order poles, algorithms are proposed in two directions. One is to conjecture new rules, and the other is to use the cross-ratio identity method. In…
Feynman integrands are constructed as Hida distributions. For our approach we first have to construct solutions to a corresponding Schroedinger equation with time-dependent potential. This is done by a generalization of the Doss approach to…
Many multi-loop calculations make use of integration by parts relations to reduce the large number of complicated Feynman integrals that arise in such calculations to a simpler basis of master integrals. Recently, Gluza, Kajda, and Kosower…
In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the integration-by-part (IBP) method in the momentum space. Tensor integrals can directly be…
A new type of integral representation is proposed for the propagators of the massive Klein-Gordon field minimally coupled to the gravity of the de Sitter expanding universe. This representation encapsulates the effects of the Heaviside step…
We will derive a rigorous real time propagator for the Non-relativistic Quantum Mechanic $L^2$ transition probability amplitude and for the Non-relativistic wave function. The propagator will be explicitly given in terms of the time…
Building on the idea of numerically integrating differential equations satisfied by Feynman integrals, we propose a novel strategy for handling branch cuts within a numerical framework. We develop an integrator capable of evaluating a basis…
Using a recent path integral representation for the T-matrix in nonrelativistic potential scattering we investigate new variational approximations in this framework. By means of the Feynman-Jensen variational principle and the most general…
We present a new method for the numerical evaluation of loop integrals which is based on the Feynman Tree Theorem. The loop integrals are replaced by phase-space integration over fictitious extra on-shell particles. This integration can be…
We revisit the idea of numerically integrating the differential form of Feynman integrals. With a novel approach for the treatment of branch cuts, we develop an integrator capable of evaluating a basis of master integrals in double and…
An elegant unified web for amplitudes of various theories was given by Cachazo, He and Yuan in the CHY framework a few years ago. Recently, similar web has also been constructed by Cheung, Shen and Wen, which relies on a set of differential…
We describe the unitarity approach for the numerical computation of two-loop integral coefficients of scattering amplitudes. It is well known that the leading propagator singularities of an amplitude's integrand are related to products of…
The Feynman Propagator of a charged particle confined to an anisotropic Harmonic Oscillator potential and moving in a crossed electromagnetic field is calculated in a conceptually new way. The calculation is based on the expansion of the…
We derive novel recursion relations for all loop amplitude integrands of planar, maximally supersymmetric Yang-Mills theory in terms of unitarity-like `cuts' obtained via sequences of BCFW deformations in momentum-twistor space.
We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite interval at zero density. $R$-matrix and monodromy matrix are obtained as limits from their known counterparts on the finite interval.…
In this thesis, we study the three-loop QCD form factors. After an introduction and a discussion of the physics motivation, we generate the quark form factor using Qgraf. We then show how to bring the Feynman integrals into a unique form by…