Related papers: Direct Expression for One-Loop Tensor Reduction wi…
We study approximation by arbitrary linear combinations of $n$ translates of a single function of periodic functions. We construct some linear methods of this approximation for univariate functions in the class induced by the convolution…
Assume that f is a strict convex function with a unique minimum in R^n. We divide the vector of n-variables to d groups of vector subvariables with d at least two. We assume that we can find the partial minimum of f with respect to each…
New explicit expressions are derived for the one-loop two-point Feynman integral with arbitrary external momentum and masses $m_1^2$ and $m_2^2$ in D dimensions. The results are given in terms of Appell functions, manifestly symmetric with…
We illustrate a rigorous approach to express the totally symmetric isotropic tensors of arbitrary rank in the $n$-dimensional Euclidean space as a linear combination of products of Kronecker deltas. By making full use of the symmetries, one…
We study perturbatively the (conformal) WZNW model. At one loop we compute one-particle irreducible two- and three-point current correlation functions, both in the conventional version and in the classically equivalent, chiral, nonlocal,…
Tensor numerical methods, based on the rank-structured tensor representation of $d$-variate functions and operators, are designed to provide $O(dn)$ complexity of numerical calculations on $n^{\otimes d }$ grids contrary to $O(n^d)$ scaling…
It is well known that forward limits of tree-level amplitudes (and those trivalent diagrams they consist of) produce one-loop amplitudes and trivalent diagrams with propagators linear in the loop momentum. They naturally arise from one-loop…
A Lorentz and gauge symmetry preserving regularization method is proposed in 4 dimension based on momentum cutoff. We use the conditions of gauge invariance or freedom of shift of the loop-momentum to define the evaluation of the terms…
Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…
One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
We analyze the decomposition of tensor products between infinite dimensional (unitary) and finite-dimensional (non-unitary) representations of SL(2,R). Using classical results on indefinite inner product spaces, we derive explicit…
By further examining the symmetry of external momenta and masses in Feynman integrals, we fulfilled the method proposed by Battistel and Dallabona, and showed that recursion relations in this method can be applied to simplify Feynman…
Given a Feynman parameter integral, depending on a single discrete variable $N$ and a real parameter $\epsilon$, we discuss a new algorithmic framework to compute the first coefficients of its Laurent series expansion in $\epsilon$. In a…
The Fourier coefficients of a negative weight eta-quotient, in many particular cases, and after Sussman in general, are known to be expressible by Hardy-Ramanujan-Rademacher type series. We show that the central terms of the coefficients of…
An algorithm for calculating two-loop propagator type Feynman diagrams with arbitrary masses and external momentum is proposed. Recurrence relations allowing to express any scalar integral in terms of basic integrals are given. A minimal…
We present a systematic method for reducing an arbitrary one-loop N-point massless Feynman integral with generic 4-dimensional momenta to a set comprised of eight fundamental scalar integrals: six box integrals in D=6, a triangle integral…
In this paper, the notion of strongly typed language will be borrowed from the field of computer programming to introduce a calculational framework for linear algebra and tensor calculus for the purpose of detecting errors resulting from…
We present a semi-analytic method for the integrand reduction of one-loop amplitudes, based on the systematic application of the Laurent expansions to the integrand-decomposition. In the asymptotic limit, the coefficients of the master…
A recursive algebraic method which allows to obtain the Feynman or Schwinger parametric representation of a generic L-loops and (E+1) external lines diagram, in a scalar $\phi ^{3}\oplus \phi ^{4}$ theory, is presented. The representation…