Related papers: Differential Reductions and Cosmological Correlati…
We report on three improvements in the context of Feynman integral reduction and $\varepsilon$-factorised differential equations: Firstly, we show that with a specific choice of prefactors, we trivialise the $\varepsilon$-dependence of the…
The degree by which a function can be differentiated need not be restricted to integer values. Usually most of the field equations of physics are taken to be second order, curiosity asks what happens if this is only approximately the case…
There is a constrained-WZNW--Toda theory for any simple Lie algebra equipped with an integral gradation. It is explained how the different approaches to these dynamical systems are related by gauge transformations. Combining Gauss…
Generalizing the main result of [Aparicio-Monforte A., Compoint E., Weil J.-A., J. Pure Appl. Algebra 217 (2013), 1504-1516], we prove that a linear differential system is in reduced form in the sense of Kolchin and Kovacic if and only if…
We examine the reduction process of a system of second-order ordinary differential equations which is invariant under a Lie group action. With the aid of connection theory, we explain why the associated vector field decomposes in three…
We elaborate on the connection between Gel'fand-Kapranov-Zelevinsky systems, de Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman integrals. We propose a novel, more efficient algorithm to compute Macaulay…
Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints.
Correlation functions of gauged WZNW models are shown to satisfy a differential equation, which is a gauge generalization of the Knizhnik-Zamolodchikov equation.
We present a comprehensive pedagogical introduction to the dimensional reduction protocol (DRP), a versatile framework for analyzing instabilities and critical points in interacting fermionic systems. The DRP simplifies the study of…
Symmetry reductions of systems of two nonlinear partial differential equations are studied. We find ansatzes reducing system of partial differential equations to system of ordinary differential equations. The method is applied to system…
Quantization in the minisuperspace of non minimal scalar-tensor theories leads to a partial differential equation which is non separable. Through a conformal transformation we can recast the Wheeler-DeWitt equation in an integrable form,…
In this work, we investigate how cosmological correlators can be reconstructed by applying the momentum-space dispersion formula to their discontinuities, treating them as functions of momentum variables associated with the corresponding de…
Using diffeomorphism group vector fields on $\mathbb{C}$-multiplied tori and the related Lie-algebraic structures, we study multi-dimensional dispersionless integrable systems that describe conformal structure generating equations of…
We define a system of "dynamical" differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra $\mathbf{g}$. These are equations on a function of $n$…
For a system of partial differential equations admitting point, contact, or higher symmetries, the framework of invariant reduction systematically computes how invariant geometric structures, such as conservation laws, presymplectic…
The $\varepsilon$-form of a system of differential equations for Feynman integrals has led to tremendeous progress in our abilities to compute Feynman integrals, as long as they fall into the class of multiple polylogarithms. It is…
Integer relation algorithms can convert numerical results for Feynman integrals to exact evaluations, when one has reason to suspect the existence of reductions to linear combinations of a basis, with rational or algebraic coefficients.…
It is known that in Friedmann-Lemaitre-Robertson-Walker cosmology one has more number of dynamical equations, compared to the number of unknown variables. This fact makes some equations redundant. The situation becomes complicated because…
We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…