Related papers: A New Framework for Higher Loop Witten Diagrams

In this work, building up on [1] we present momentum space Ward identities related to broken higher spin symmetry as an alternate approach to computing correlators of spinning operators in interacting theories such as the quasi-fermionic…

We construct and classify superconformally covariant differential operators defined on N=2 super Riemann surfaces. By contrast to the N=1 theory, these operators give rise to partial rather than ordinary differential equations which leads…

The aim of this article is to prove a Beals type characterization theorem for pseudodifferential operators in Wiener spaces. The definition of pseudodifferential operators in Wiener spaces and a Calder\'on-Vaillancourt type result appear in…

This paper introduces a differentiable semantic reasoner, where rules are presented as a relevant set of graph transformations. These rules can be written manually or inferred by a set of facts and goals presented as a training set. While…

Study of correlation functions in AdS/CFT and in-in correlators in de Sitter space often requires the computation of Witten diagrams. Due to the complexity of evaluating radial integrals for these correlators, several indirect approaches…

We address a linearity problem for differentiable vectors in representations of infinite-dimensional Lie groups on locally convex spaces, which is similar to the linearity problem for the directional derivatives of functions.

Integral representations are derived for the parabolic cylinder functions $U(a,x)$, $V(a,x)$ and $W(a,x)$ and their derivatives. The new integrals will be used in numerical algorithms based on quadrature. They follow from contour integrals…

We study boundary value problems for some differential operators on Euclidean space and the Heisenberg group which are invariant under the conformal group of a Euclidean subspace resp. Heisenberg subgroup. These operators are shown to be…

Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…

This article develops new techniques for understanding the relationship between the three different mathematical formulations of two-dimensional chiral conformal field theory: conformal nets (axiomatizing local observables), vertex operator…

(This short article is a continuation of a longer, review work, in the same volume of Proceedings, by Ashtekar, Marolf and Mour\~ao [gr-qc/9403042]. All the details and other results are to be found in joint papers of the author with Abhay…

This paper considers the open challenge of identifying complete, concise, and explainable quantitative microstructure representations for disordered heterogeneous material systems. Completeness and conciseness have been achieved through…

This paper gives a geometric interpretation of the notion of quasi-symmetric representation and uses this to show that the discriminant locus associated to such a representation is a hyperplane arrangement. Moreover, we identify this…

We describe the application of differential reduction algorithms for Feynman Diagram calculation. We illustrate the procedure in the context of generalized hypergeometric functions, and give an example for a type of q-loop bubble diagram.

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

Effectively handling the nonlocal pseudo-differential term plays an impor?tant role in solving the Wigner equation with high accuracy. This paper systematically analyzes and compares numerical treatments of the pseudo-differential term…

The Weil representation of the symplectic group associated to a finite abelian group of odd order is shown to have a multiplicity-free decomposition. When the abelian group is p-primary, the irreducible representations occurring in the Weil…

Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and…

The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…

In this paper, using the Weyl-Wigner-Moyal formalism for quantum mechanics, we develop a {\it quantum-deformed} exterior calculus on the phase-space of an arbitrary hamiltonian system. Introducing additional bosonic and fermionic…