Related papers: Algorithmic transformation of multi-loop master in…
We present RandomizedCCA, a randomized algorithm for computing canonical analysis, suitable for large datasets stored either out of core or on a distributed file system. Accurate results can be obtained in as few as two data passes, which…
We compute icanonical basis of the quasi-split rank one modified iquantum group, by obtaining explicit transition matrices among the icanonical basis, monomial basis, and standardized canonical basis; all these bases can be naturally…
Let $\C$ be a sequence of multisets of subspaces of a vector space $\F_q^k$. We describe a practical algorithm which computes a canonical form and the stabilizer of $\C$ under the group action of the general semilinear group. It allows us…
We show how a large class of Feynman integrals can be efficiently reduced to master integrals by suitable covariant differentiation on the vector space dual to the one spanned by the master integrals. The connections needed in the covariant…
The method of continuous canonical transformation is applied to the double exchange model with a purpose to eliminate the interaction term responsible for non conservation of magnon number. Set of differential equations for the effective…
In these proceedings we will review recent progress in applying ideas from the mathematical framework of twisted cohomology to the study of canonical differential equations for Feynman integrals. Firstly, we will show how the intersection…
In this paper, we elaborate on the connection between leading singularities and canonical bases of Feynman integrals beyond polylogarithms. We start by discussing a notion of leading singularities in dimensional regularization, which can be…
Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…
We use recent results on algorithms for Markov decision problems to show that a canonical form for a generalized P-matrix can be computed, in some important cases, by a strongly polynomial algorithm.
An elementary presentation of the methods for the canonical quantization of constraint systems with Fermi variables is given. The emphasis is on the subtleties of the construction of an appropriate classical bracket that could be…
In this note we provide an algorithm for computing the fractional integrals of orthogonal polynomials, which is more stable than that using the expression of the polynomials w.r.t. the canonical basis. This algorithm is aimed at solving…
Canonical correlation analysis (CCA) is a technique to find statistical dependencies between a pair of multivariate data. However, its application to high dimensional data is limited due to the resulting time complexity. While the…
A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…
We evaluate the three-loop five-point pentagon-box-box massless integral family in the dimensional regularization scheme, via canonical differential equation. We use tools from computational algebraic geometry to enable the necessary…
The reduction of Feynman integrals to master integrals is an algebraic problem that requires algorithmic approaches at the modern level of calculations. Straightforward applications of the classical Buchberger algorithm to construct…
In this paper we describe a method of calculation of master integrals based on the solution of systems of difference equations in one variable. Various explicit examples are given, as well as the generalization to arbitrary diagrams.
The standard procedure when evaluating integrals of a given family of Feynman integrals, corresponding to some Feynman graph, is to construct an algorithm which provides the possibility to write any particular integral as a linear…
We apply a recently suggested new strategy to solve differential equations for master integrals for families of Feynman integrals. After a set of master integrals has been found using the integration-by-parts method, the crucial point of…
A common approach to minimizing the cost of quantum computations is by transforming a quantum system into a basis that can be optimally truncated. Here, we derive classical equations of motion subjected to similar unitary transformations,…
The reduction of Feynman integrals to a basis of master integrals plays a crucial role for many high-precision calculations and Kira is one of the leading tools for this task. In these proceedings we discuss some of the new features and…