Related papers: Representations of the Flat Space Wavefunction
We construct a position-space cosmological perturbation theory around spatially flat Friedmann-Lema\^itre-Robertson-Walker geometries that allows to model localized primordial sources of gravitational waves. The equations of motion are…
Let $\mathbb F$ be a finite field and let $\mathcal A$ and $\mathcal B$ be vector spaces of $\mathbb F$-valued continuous functions defined on locally compact spaces $X$ and $Y$, respectively. We look at the representation of linear…
We introduce fractional realizations of a graph degree sequence and a closely associated convex polytope. Simple graph realizations correspond to a subset of the vertices of this polytope. We describe properties of the polytope vertices and…
Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can be used for a variety of…
Since the discovery of quantum mechanics, the fact that the wavefunction is defined on the $3\mathbf{n}$-dimensional configuration space rather than on the $3$-dimensional space has seemed uncanny to many, including Schr\"odinger, Lorentz,…
This paper proposes a new approach to deriving a finite particle content, suitable for the construction of a gauge theory. Specifically, the outlined construction generates a finite set of irreducible gauge representations, which are…
A partial complement of the graph $G$ is a graph obtained from $G$ by complementing all the edges in one of its induced subgraphs. We study the following algorithmic question: for a given graph $G$ and graph class $\mathcal{G}$, is there a…
For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…
The quantum theory of U(1) connections admits a diffeomorphism invariant representation in which the electric flux through any surface is quantized. This representation is the analog of the representation of quantum SU(2) theory used in…
Applying the Helmholtz Decomposition theorem to linearized General Relativity leads to a gauge-invariant formulation where the transverse-traceless part of the metric perturbation describes gravitational waves in matter. Gravitational waves…
Given a finitely-generated group $\pi$ and a linear algebraic group $G$, the representation variety Hom$(\pi,G)$ has a natural filtration by the characteristic varieties associated to a rational representation of $G$. Its algebraic…
In this letter a new formula for light deflection is derived using only physically observable concepts. The general result is specialized to cosmological perturbation theory and expressed in terms of gauge--invariant perturbation variables.…
We introduce the standard decomposition, a way of decomposing a labeled graph into a sum of certain labeled subgraphs. We motivate this graph-theoretic concept by relating it to Connect Four decompositions of standard sets. We prove that…
The global symmetry data of a $D$-dimensional absolute quantum field theory can sometimes be packaged in terms of a $(D+1)$-dimensional bulk system obtained by extending along an interval, with a relative QFT$_D$ at one end and suitable…
Spaces of harmonic functions in upper half-space with controlled growth near the boundary are described in terms of multiresolution approximations. The results are applied to prove the law of the iterated logarithm for the oscillation of…
It is known, that every function on the unit sphere in $\bbr^n$, which is invariant under rotations about some coordinate axis, is completely determined by a function of one variable. Similar results, when invariance of a function reduces…
We propose a functional integral representation for Archimedean L-factors given by products of Gamma-functions. The corresponding functional integral arises in the description of type A equivariant topological linear sigma model on a disk.…
We show that spherical Whittaker functions on an $n$-fold cover of the general linear group arise naturally from the quantum Fock space representation of $U_q(\widehat{\mathfrak{sl}}(n))$ introduced by Kashiwara, Miwa and Stern (KMS). We…
The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From…
We review work on `decomposition,' a property of two-dimensional theories with 1-form symmetries and, more generally, d-dimensional theories with (d-1)-form symmetries. Decomposition is the observation that such quantum field theories are…