Related papers: Direct Systems of Spherical Functions and Represen…
This paper is a continuation of [2], where we complete our partial proof of the Deser-Schwimmer conjecture on the structure of ``global conformal invariants''. Our theorem deals with such invariants P(g^n) that locally depend only on the…
The long-standing problem of representing the general massive one-loop Feynman integral as a meromorphic function of the space-time dimension $d$ has been solved for the basis of scalar one- to four-point functions with indices one. In 2003…
We define the representation ring of a saturated fusion system $\mathcal F$ as the Grothendieck ring of the semiring of $\mathcal F$-stable representations, and study the dimension functions of $\mathcal F$-stable representations using the…
The spinor representation is developed for conformal immersions of Riemann surfaces into space. We adapt the approach of Dennis Sullivan, which treats a spin structure on a Riemann surface M as a complex line bundle S whose square is the…
We give a new construction of the spherical Witt vector functor of Lurie and Burklund-Schlank-Yuan and extend it to nonconnective objects using synthetic spectra and recent work of Holeman. The spherical Witt vectors are used to build…
We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show…
We present an alternative formulation of quantum mechanical angular momentum, based on spatial wavefunctions that depend on the Euler angles $\phi, \theta, \chi$, and have an additional internal projection $n$. The wavefunctions are Wigner…
We characterize the image of radial positive measures $\theta$'s on a harmonic $NA$ group $S$ which satisfies $\int_S\phi_0(x)\,d\theta(x)<\infty$ under the spherical transform, where $\phi_0$ is the elementary spherical function.
Looking for a quantum field theory model of Archimedean algebraic geometry a class of infinite-dimensional integral representations of classical special functions was introduced. Precisely the special functions such as Whittaker functions…
We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of…
Graphical functions have emerged as a powerful framework for evaluating multi-loop Feynman integrals in perturbative quantum field theory. Defined as massless three-point position-space integrals, they reveal rich analytic structures and…
We develop a general framework for isotropic functional Gaussian fields on the $d$-dimensional sphere $\mathbb{S}^{d}$, where the field takes values in a separable Hilbert space $\mathcal{H}$. We establish an operator-valued extension of…
We generalize a space-time-symmetric (STS) extension of non-relativistic quantum mechanics (QM) to describe a particle moving in three spatial dimensions. In addition to the conventional time-conditional (Schr\"odinger) wave function…
We consider the problem of graph-matching on a network of 3D shapes with uncertainty quantification. We assume that the pairwise shape correspondences are efficiently represented as \emph{functional maps}, that match real-valued functions…
Gravitational theories generated from Lagrangians of the form f(R) are considered. The spherically symmetric solutions to these equations are discussed, paying particular attention to features that differ from the standard Schwarzschild…
Let G/K be an irreducible Hermitian symmetric space and let D be a K-invariant domain in G/K. In this paper we characterize several classes of K-invariant plurisubharmonic functions on D in terms of their restrictions to a slice…
We study non-linear functionals, including quasi-linear functionals, p-conic quasi-linear functionals, d-functionals, r-functionals, and their relationships to deficient topological measures and topological measures on locally compact…
We introduce the space $X$ of quaternion hermitian forms of size $n$ on a ${\mathfrak p}$-adic field with odd residual characteristic, and define typical spherical functions $\omega(x;s)$ on $X$ and give their induction formula on sizes by…
Let $F$ be a non-Archimedean local field of characteristic $0$ and $G=Sp(4,F)$. Let $(\pi,W)$ be an irreducible smooth self-dual representation $G$. The space $W$ of $\pi$ admits a non-degenerate $G$-invariant bilinear form $(\,,\,)$ which…
In the previous paper [25], Stolarsky's invariance principle, known for point distributions on the Euclidean spheres [27], has been extended to the real, complex, and quaternionic projective spaces and the octonionic projective plane.…