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A finitely-additive measure $\lambda $ on an infinite-dimensional real Hilbert space $E$ which is invariant with respect to shifts and orthogonal mappings has been defined. This measure can be considered as the analog of the Lebesgue…
We compute the Weyl anomaly for an abelian Wilson surface by using a regularization that respects the gauge invariance. We then study the loop space on which lives a one-form connection. We restrict ourselves to the subsector consisting of…
Let $(W,H,\mu)$ be the classical Wiener space, assume that $U=I_W+u$ is an adapted perturbation of identity where the perturbation $u$ is an equivalence class w.r.to the Wiener measure. We study several necessary and sufficient conditions…
We develop a calculus of variations for functionals on certain spaces of conformal maps. Such a space \Omega\ is composed of all maps that are conformal on domains containing a fix compact annular set of the Riemann sphere, and that are…
Measurement incompatibility--the impossibility of jointly measuring certain quantum observables--is a fundamental resource for quantum information processing. We develop a graph-theoretic framework for quantifying this resource for large…
For vacuum Maxwell theory in four dimensions, a supplementary condition exists (due to Eastwood and Singer) which is invariant under conformal rescalings of the metric, in agreement with the conformal symmetry of the Maxwell equations.…
We prove several versions of Driver's integration by parts formula for the horizontal Wiener measure on a totally geodesic Riemannian foliation and prove that the horizontal Wiener measure has a quasi-invariance property with respect to…
We apply weighted Mourre commutator theory to prove the limiting absorption principle for the discrete Schr{\"o}dinger operator perturbed by the sum of a Wigner-von Neumann and long-range type potential. In particular, this implies a new…
We study Weil-Petersson (WP) geodesics with narrow end invariant and develop techniques to control length-functions and twist parameters along them and prescribe their itinerary in the moduli space of Riemann surfaces. This class of…
Scale-invariant actions in arbitrary dimensions are investigated in curved space to clarify the relation between scale-, Weyl- and conformal invariance on the classical level. The global Weyl-group is gauged. Then the class of actions is…
We propose a method for the calculation of vacuum expectation values (VEVs) given a non-trivial, long-distance vacuum wave functional (VWF) of the kind that arises, for example, in variational calculations. The VEV is written in terms of a…
In this paper we study the expectation value of deformations of the circular Wilson loop in ${\cal N}=4$ super Yang-Mills theory. The leading order deformation, known as the Bremsstrahlung function, can be obtained exactly from…
A classical result of Norbert Wiener characterises doubly shift-invariant subspaces for square integrable functions on the unit circle with respect to a finite positive Borel measure $\mu$, as being the ranges of the multiplication maps…
Deser and Nepomechie established a relationship between masslessness and rigid conformal invariance by coupling to a background metric and demanding local Weyl invariance, a method which applies neither to massive theories nor theories…
We study the properties of reflectionless measures for a Calder\'{o}n-Zygmund operator T. Roughly speaking, these are measures $\mu$ for which T(\mu) vanishes (in a weak sense) on the support of the measure. We describe the relationship…
Given a finitely connected region $\Omega$ of the Riemann sphere whose complement consists of $m$ mutually disjoint closed disks $\bar{U}_j$, the random homeomorphism $h_j$ on the boundary component $\partial U_j$ is constructed using the…
Lorentz invariance is a cornerstone of modern physics, yet its possible violation remains both theoretically intriguing and experimentally significant. In this work, using quantum electrodynamics as an example, we explore how Lorentz…
The covariantization procedure is usually referred to the translation operator, that is the derivative. Here we introduce a general method to covariantize arbitrary differential operators, such as the ones defining the fundamental group of…
We introduce a concept of Clebsch confinement related to unbroken gauge invariance and study Clebsch instantons: singular vorticity sheets with nontrivial helicity. This is realization of the "Instantons and intermittency" program we…
A family of diffeomorphism-invariant Seiberg--Witten deformations of gravity is constructed. In a first step Seiberg--Witten maps for an SO(1,3) gauge symmetry are obtained for constant deformation parameters. This includes maps for the…