Related papers: A New Framework for Higher Loop Witten Diagrams
We uncover a combinatorial structure governing the differential equations satisfied by wavefunction coefficients of scalar fields with generic masses in de Sitter space. Using an integral representation of the massive mode functions, we…
A notion of differentiability is being proposed for maps between Wasserstein spaces of order 2 of smooth, connected and complete Riemannian manifolds. Due to the nature of the tangent space construction on Wasserstein spaces, we only give a…
The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The…
We present an analytic study of conformal field theories on the real projective space $\mathbb{RP}^d$, focusing on the two-point functions of scalar operators. Due to the partially broken conformal symmetry, these are non-trivial functions…
We consider the problem of learning discriminative representations for data in a high-dimensional space with distribution supported on or around multiple low-dimensional linear subspaces. That is, we wish to compute a linear injective map…
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…
A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
We survey a new application of the Weil representation to construct a canonical basis of eigenvectors for the discrete Fourier transform (DFT). The transition matrix from the standard basis to the canonical basis defines a novel transform…
In this paper, we consider the locally convex spaces of entire functions with growth given by proximate orders, and study the representation as a differential operator of a continuous homomorphism from such a space to another one. As a…
In this paper we discuss geodesic Witten diagrams in generic holographic conformal field theories with boundary or defect. Boundary CFTs allow two different decompositions of two-point functions into conformal blocks: boundary channel and…
In this paper we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This…
Deep representation learning is a subfield of machine learning that focuses on learning meaningful and useful representations of data through deep neural networks. However, existing methods for semantic classification typically employ…
Solitons in two-dimensional quantum field theory exhibit patterns of degeneracies and associated selection rules on scattering amplitudes. We develop a representation theory that captures these intriguing features of solitons. This…
Higher order derivatives of functions are structured high dimensional objects which lend themselves to many alternative representations, with the most popular being multi-index, matrix and tensor representations. The choice between them…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
Conformal blocks are the fundamental, theory-independent building blocks in any CFT, so it is important to understand their holographic representation in the context of AdS/CFT. We describe how to systematically extract the holographic…
We introduce an alternative formalization of curved spaces in which the concept of a pointwise affine space, as defined here, replaces that of a manifold. New or modified definitions of familiar notions from differential geometry such as…
We outline an abstract approach to the pseudo-differential Weyl calculus for operators in function spaces in infinitely many variables. Our earlier approach to the Weyl calculus for Lie group representations is extended to the case of…
Differential geometry may be generalized to allow infinitesimals to any order. The purpose of the present contribution is to show that the theory so developed expands received geometrical ideas in an interesting way, rich in potential for…