Related papers: Vertical Integration from the Large Hilbert Space
We introduce a new approach to the spectral equivalence of Gaussian processes and fields, based on the methods of operator theory in Hilbert space. Besides several new results including identities in law of quadratic norms for integrated…
Phase retrieval in real or complex Hilbert spaces is the task of recovering a vector, up to an overall unimodular multiplicative constant, from magnitudes of linear measurements. In this paper, we assume that the vector is normalized, but…
This article describes the implementation of the joint motion estimation and image reconstruction framework presented by Burger, Dirks and Sch\"onlieb and extends this framework to large-scale motion between consecutive image frames. The…
For the closed superstring, spin fields and bi-spinor states are defined directly in four spacetime dimensions. Explicit operator product expansions are given, including those for the internal superconformal field theory, which are…
Given a finite-dimensional inner product space $V$ and a group $G$ of isometries, we consider the problem of embedding the orbit space $V/G$ into a Hilbert space in a way that preserves the quotient metric as well as possible. This inquiry…
Celestial holography provides a promising avenue to studying bulk scattering in flat spacetime from the perspective of boundary celestial conformal field theory (CCFT). A key ingredient in connecting the two sides is the celestial…
We discuss systematic extensions of the standard (St{\"o}rmer-Verlet) splitting method for differential equations of Hamiltonian mechanics, with relative accuracy of order $\tau^2$ for a timestep of length $\tau$, to higher orders in…
Insightful visualization of multidimensional scalar fields, in particular parameter spaces, is key to many fields in computational science and engineering. We propose a principal component-based approach to visualize such fields that…
The Bethe-Salpeter Equation for a two-scalar, S-wave bound system, interacting through a massive scalar, is investigated within the ladder approximation. By assuming a Nakanishi integral representation of the Bethe-Salpeter amplitude, one…
The spinor-helicity formalism is an essential technique of the amplitudes community. We draw on this method to construct a scheme for classifying higher-dimensional spacetimes in the style of the four-dimensional Petrov classification and…
In this paper, our aim is to introduce the concept of a frame in n-Hilbert space and describe some of their properties. We further discuss tight frame relative to n-Hilbert space. At the end, we study the relationship between frame and…
Consider a physical system for which a mathematically rigorous geometric quantization procedure exists. Now subject the system to a finite set of irreducible first class (bosonic) constraints. It is shown that there is a mathematically…
In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral…
The transition amplitudes between coherent states on a coherent state manifold are expressed in terms of the embedding of the coherent state manifold into a projective Hilbert space. Consequences for the dimension of projective Hilbert…
We examine, in a quantum mechanical setting, the Hilbert space representation of the BRST symmetry associated with Schwinger-Keldysh path integrals. This structure had been postulated to encode important constraints on influence functionals…
We present a practical implementation of the perturbation theory derived by Lynden-Bell (2015) for describing, to arbitrary precision, the orbit of a particle in an arbitrary spherically-symmetric potential. Our implementation corrects…
Non-Hermitian systems exploiting the synergy between gain and loss have recently become the focus of interest to discover novel physical phenomena. The spatial symmetry breaking in such systems allows tailoring the wave propagation at will.…
General expository paper concerning topics in Hilbert spaces, spectral theory, and harmonic analysis. The preliminary section includes basic Banach algebra and Hilbert space theory with a digression on Riesz bases. The second and third…
This article, which is a review with substantial original material, is meant to offer a comprehensive description of the superfield representations of the BRST and anti-BRST algebras and their applications to some field-theoretic topics.…
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind).…