Related papers: Colour-Twist Operators I: Spectrum and Wave Functi…
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…
We describe how to construct generalized string-net models, a class of exactly solvable lattice models that realize a large family of 2D topologically ordered phases of matter. The ground states of these models can be thought of as…
We consider several aspects of unitary higher-dimensional conformal field theories (CFTs). We first study massive deformations that trigger a flow to a gapped phase. Deep inelastic scattering in the gapped phase leads to a convexity…
We extend to twisted spectral triples the fluctuations of the metric, as well as their gauge transformations. The former are bounded perturbations of the Dirac operator that arise when a spectral triple is exported between Morita equivalent…
In this article, we prove the following spectral theorem for right linear normal operators (need not to be bounded) in quaternionic Hilbert spaces: Let $T$ be an unbounded right quaternionic linear normal operator in a quaternionic Hilbert…
We study an abstract family of asymptotically degenerating variational problems. Those are natural generalisations of families of problems emerging upon application of a rescaled Floquet-Bloch-Gelfand transform to resolvent problems for…
Using general principles in the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…
It was recently shown that the string theory duals of certain deformations of the N=4 gauge theory can be obtained by a combination of T-duality transformations and coordinate shifts. Here we work out the corresponding procedure of twisting…
We study novel conformal twist defects in 4d Maxwell theory, around which electric and magnetic fields are exchanged. These are codimension-2 defects living at the end of topological defects for certain non-invertible global symmetries. We…
In the present paper we describe the procedure of the Q-operators construction for the q-deformed model, described by the Lax operator, which is important to formulate the Bethe ansatz for the Sin-Gordon model. This Lax operator can also be…
The notion of the wave spectrum of a semi-bounded symmetric operator was introduced by one of the authors in 2013. The wave spectrum is a topological space determined by the operator in a canonical way. The definition uses a dynamical…
We study non-perturbative interpolating functions to probe the physics of anomalous dimensions associated with twist-two operators in ${\cal N}=4$ SYM of finite and infinite spin. Compared to previous studies, the novel result of this paper…
The N-extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even N one can identify the 1D…
The spectral shift function of a pair of self-adjoint operators is expressed via an abstract operator valued Titchmarsh--Weyl $m$-function. This general result is applied to different self-adjoint realizations of second-order elliptic…
In this paper, we study one of the fundamental notions in dynamical systems, the shadowing of invertible (bounded and linear) operators on a Hilbert space. Although the problem of finding a spectral characterization for shadowing has been…
Building on arXiv:1902.03807, this paper develops a unifying study on the boundedness properties of several representative classes of hybrid operators, i.e. operators that enjoy both zero and non-zero curvature features. Specifically, via…
Consider a reference homogeneous and isotropic electromagnetic waveguide with a simply connected cross-section embedded in a perfect conductor. In this setting, when the waveguide is straight, the spectrum of the associated self-adjoint…
In this article combinatorial aspects of normal ordering annihilation and creation operators of a multi-mode boson system are discussed. The modes are assumed to be coupled since otherwise the problem of normal ordering is reduced to the…
An operator $T\in B(H)$ is said to satisfy property ($UW${\scriptsize \it{E}}) if the complement in the approximate point spectrum of the essential approximate point spectrum coincides with the isolated eigenvalues of the spectrum. Via the…
The modern approach to $m$-form global symmetries in a $d$-dimensional quantum field theory (QFT) entails specifying dimension $d-m-1$ topological generalized symmetry operators which non-trivially link with $m$-dimensional defect…