Related papers: Smeared and unsmeared chiral vertex operators
We consider the Schroedinger operator with a complex delta interaction supported by two parallel hypersurfaces in the Euclidean space of any dimension. We analyse spectral properties of the system in the limit when the distance between the…
In the present paper we continue our study of non-commutative operator graphs in infinite-dimensional spaces. We consider examples of the non-commutative operator graphs generated by resolutions of identity corresponding to the…
We study several classes of indecomposable representations of quivers on infinite-dimensional Hilbert spaces and their relation. Many examples are constructed using strongly irreducible operators. Some problems in operator theory are…
We study chiral algebra in the reduction of 3D $\mathcal{N} = 2 $ supersymmetric gauge theories on an interval with the $\mathcal{N}=(0,2)$ Dirichlet boundary conditions on both ends. By invoking the 3D ``twisted formalism'' and the 2D…
In this work we realize the 3 + 1 dimensional non-invertible ${\mathbb{Z}}_N$ chiral symmetry generator as an operator in a many body lattice Hilbert space. A crucial ingredient in our construction is the use of infinite dimensional $U(1)$…
We propose a method for the spectral analysis of unbounded operator matrices in a general setting which fully abstains from standard perturbative arguments. Rather than requiring the matrix to act in a Hilbert space $\mathcal{H}$, we extend…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
The spectral and scattering theory for 1-dimensional Dirac operators with mass $m$ and with zero-range interactions are fully investigated. Explicit expressions for the wave operators and for the scattering operator are provided. These new…
Semi-infinite forms on the moduli spaces of genus-zero Riemann surfaces with punctures and local coordinates are introduced. A partial operad for semi-infinite forms is constructed. Using semi-infinite forms and motivated by a partial…
Recently, the generating system that describes interacting symmetric higher-spin gauge fields at the level of equations of motion was proposed. The interaction vertices it offers are 'off the mass shell' unless constrained by the prescribed…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems through systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
In this paper, we consider \emph{unbounded} weighted composition operators acting on Fock space, and investigate some important properties of these operators, such as $\calC$-selfadjoint (with respect to weighted composition conjugations),…
We initiate the study of the small scale geometry of operator spaces. The authors have previously shown that a map between operator spaces which is completely coarse (that is, the sequence of its amplifications is equi-coarse) must be…
We construct quantized free superfields and represent them as operator-valued distributions in Fock space starting with Majorana fields. The perturbative construction of the S-matrix for interacting theories is carried through by extending…
Boundary operators and boundary ground states in sine-Gordon model with a fixed boundary condition are studied using bosonization and q-deformed oscillators.We also obtain the form-factors of this model.
The scope of this text is to study a process that induces another proof of the Spectral Embedding Theorem: that any densely defined symmetric operator can be extended by a multiplication operator through an embedding of the Hilbert space…
We prove and apply two theorems: First, a quantitative, scale-free unique continuation estimate for functions in a spectral subspace of a Schr\"odinger operator on a bounded or unbounded domain, second, a perturbation and lifting estimate…
Short distance scaling limits of a class of integrable models on two-dimensional Minkowski space are considered in the algebraic framework of quantum field theory. Making use of the wedge-local quantum fields generating these models, it is…
In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of $S$-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and…
The spectral analysis of a non-Hermitian unbounded operator appearing in quantum physics is our main concern. The properties of such an operator are essentially different from those of Hermitian Hamiltonians, namely due to spectral…