Related papers: Differential Equations for Massive Correlators
We consider scalar perturbations of energy-density for a class of cosmological models where an early phase of accelerated expansion evolves, without any fine-tuning for graceful exit, towards the standard Friedman eras of observed universe.…
We develop primal and mixed variational formulations of transport phenomena on cell complexes with simple polytope connectivity. This framework addresses materials with internal structures comprising components of different topological…
Motivated by recent evidence that equal-time correlators can be simpler than the corresponding wavefunction coefficients, we study de Sitter correlators in conformally coupled $\phi^3$ theory directly. By inverting the momentum-space…
We formulate the problem of renormalization of Feynman integrals and its relation to periods of motives in configuration space instead of momentum space. The algebro-geometric setting is provided by the wonderful compactifications of…
For correlators in $\mathcal{N}=4$ Super Yang-Mills preserving half the supersymmetry, we manifestly recast the gauge theory Feynman diagram expansion as a sum over dual closed strings. Each individual Feynman diagram maps on to a Riemann…
We propose a cosmological model which could explain, in a very natural way, the apparently periodic structures of the universe, as revealed in a series of recent observations. Our point of view is to reduce the cosmological…
We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy…
We study the algebraic and analytic structure of Feynman integrals by proposing an operation that maps an integral into pairs of integrals obtained from a master integrand and a corresponding master contour. This operation is a coaction. It…
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…
A momentum-space approach to conformal field theory offers a new perspective on cosmological correlators and better reveals the underlying connections to scattering amplitudes. This thesis explores the interplay between integral…
We elaborate on the recent idea of a direct decomposition of Feynman integrals onto a basis of master integrals on maximal cuts using intersection numbers. We begin by showing an application of the method to the derivation of contiguity…
This survey is the continuation of a series of works aimed at applying tools from Singularity Theory to Differential Equations. More precisely, we utilize the powerfull Milnor's Fibration Theory to give geometric-topological classifications…
Inflation correlators with massive exchanges are central observables of cosmological collider physics, and are also important theoretical data for us to better understand quantum field theories in dS. However, they are difficult to compute…
This work establishes a robust mathematical foundation for compositional System Dynamics modeling, leveraging category theory to formalize and enhance the representation, analysis, and composition of system models. Here, System Dynamics…
A fundamental problem from invariant theory is to describe the endomorphism algebra of multilinear functions on a representation V invariant under the action of a group G. According to Weyl's classic, a first main (later: fundamental)…
The perturbative expansion of tensorial field theories in Feynman graphs can be interpreted as weighted generating series of some piecewise linear varieties. This simple fact establishes a link between two a priori distinct fields: the…
The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super-Yang-Mills. It is dual to another complex matrix…
In this paper we provide a framework for the study of isoperimetric problems in finitely generated group, through a combinatorial study of universal covers of compact simplicial complexes. We show that, when estimating filling functions,…
Some well-known examples of constrained quantum systems commonly quantized via Feynman path integrals are re-examined using the notion of conditional integrators introduced in [1]. The examples yield some new perspectives on old results. As…
The cosmological field equations sourced by a self-interacting scalar field are dynamically equivalent to a closed system of equations obtained by applying the moment method to non-linear Schr\"odinger equations possessing an underlying…