Related papers: Haar-Type Measures on Topological Quasigroups and …
A unified expression for topological invariants has been proposed recently to describe the topological order in Dirac models belonging to any dimension and symmetry class. We uncover a correspondence between the curvature function that…
For massive and conformal quantum field theories in 1+1 dimensions with a global gauge group we consider soliton automorphisms, viz. automorphisms of the quasilocal algebra which act like two different global symmetry transformations on the…
In this m\'emoire we study quasiperiodic cocycles in semi-simple compact Lie groups. For the greatest part of our study, we will focus ourselves to one-frequency cocyles. We will prove that $C^{\infty}$ reducible cocycles are dense in the…
The Stone-von Neumann Theorem is a fundamental result which unified the competing quantum mechanical models of matrix mechanics and wave mechanics. It's mechanism of proof ultimately involved the study of unitary group representations on a…
Covariance functions are a fundamental tool for modeling the dependence structure of spatial processes. This work investigates novel constructions for covariance functions that enable the integration of anisotropies and hole effects in…
This article addresses the overlooked but crucial role of the Haar measure in solid mechanics, a concept well-established in mathematical literature but frequently misunderstood by mechanicians. The aim is to provide practical insights and…
We associate canonically a cyclic module to any Hopf algebra endowed with a modular pair, consisting of a group-like element and a character, in involution. This provides the key construct allowing to extend cyclic cohomology to Hopf…
We examine Hopf cyclic cohomology in the same context as the analysis of the geometry of loop spaces $LX$ in derived algebraic geometry and the resulting close relationship between $S^1$-equivariant quasi-coherent sheaves on $LX$ and…
We study gauging operations (or group extensions) in (smeared) boundary conformal field theories (BCFTs) and bulk conformal field theories, and their applications to various phenomena in topologically ordered systems. We apply the resultant…
Let G be a compact, connected Lie group, acting smoothly on a manifold M. Goresky-Kottwitz-MacPherson described a small Cartan model for the equivariant cohomology of M, quasi-isomorphic to the standard Cartan complex of equivariant…
Asymptotic Schur orthogonality relations are for irreducible unitary representations of locally compact groups that need not be discrete series, where $L^2$ pairing of matrix coefficients with respect to Haar measure is replaced by a limit…
We introduce cosurfaces with values in the group \(\PC_n(H)\) of \(H\)-valued reciprocal pairwise comparison matrices. The composition law is covariant on upper triangular coefficients and contravariant on lower triangular coefficients,…
Paradoxically, while the assumptions of second-order stationarity and isotropy appear outdated in light of modern spatial data, they remain remarkably robust in practice, as nonstationary methods often provide marginal improvements in…
In a recent experimental work [Z. Wu et al., Science 354, 83 (2016)], the PKU-USTC group realized a two-dimensional two-band quantum anomalous Hall model on a square Raman lattice. By quenching the atom-laser detuning of such a Raman…
We construct a class of quantum field theories depending on the data of a holomorphic Poisson structure on a piece of the underlying spacetime. The main technical tool relies on a characterization of deformations and anomalies of such…
In this paper, we consider topological semigroup actions on compact topological spaces. Under mild assumptions on the semigroup and the action, we construct a semi-direct product groupoid with a Haar system. We also show that it is…
The concept of coherence is one of cornerstones in physics. The development of quantum information science has lead to renewed interest in properly approaching the coherence at the quantum level. Various measures could be proposed to…
We give examples of (i) a simple theory with a formula (with parameters) which does not fork over the empty set but has mu measure 0 for every automorphism invariant Keisler measure mu, and (ii) a definable group G in a simple theory such…
Let $H$ be a semisimple Hopf algebras over an algebraically closed field $k$ of characteristic $0.$ We define Hopf algebraic analogues of commutators and their generalizations and show how they are related to $H',$ the Hopf algebraic…
Let \(G\) be a non-discrete, locally compact group with Haar measure \(m\). We prove that there exists a compact set \(K \subset G\) with \(m(K)=0\) such that \(KK^{-1}\) contains a neighborhood of the identity. Moreover, such a set may be…