Related papers: Defining Root-$T\overline{T}$ operator
We shall give a definition of the curvature operator for a family of weighted Bergman spaces $\{\mathcal H_t\}$ associated to a smooth family of smoothly bounded strongly pseudoconvex domains $\{D_t\}$. In order to study the boundary term…
Given a bounded linear operator $T$ on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for $T$ having certain specified algebraic or asymptotic structure. We obtain matrix representations…
In this paper, we study square functions for extension operators over finite-type, planar curves endowed with the Euclidean arclength measure. We prove new results for curves of the form $(T,\phi(T))$ where $\phi(T)$ is a polynomial of…
The time evolution operator (Schr\"odinger functional) of quantum field theory can be expressed in terms of first quantised particles moving on the orbifold $S^1/Z_2$. We give a graphical derivation of this that generalises to second…
We construct the explicit $Q$-operator incorporated with the $sl_2$-loop-algebra symmetry of the six-vertex model at roots of unity. The functional relations involving the $Q$-operator, the six-vertex transfer matrix and fusion matrices are…
$J\bar T$-deformed CFTs provide an interesting example of non-local, yet UV-complete two-dimensional QFTs that are entirely solvable. They have been recently shown to possess an infinite set of symmetries, which are a continuous deformation…
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
It is shown that the scaling operators in the conformal limit of a two-dimensional field theory have massive form factors which obey a simple factorisation property in rapidity space. This has been used to identify such operators within the…
A functional calculus on the space of (generalized) connections was recently introduced without any reference to a background metric. It is used to continue the exploration of the quantum Riemannian geometry. Operators corresponding to…
We propose that the Baxter $Q$-operator for the spin-1/2 XXZ quantum spin chain is given by the $j\to \infty$ limit of the transfer matrix with spin-$j$ (i.e., $(2j+1)$-dimensional) auxiliary space. Applying this observation to the open…
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
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…
We study Schr\"odinger operators on $\mathbb R^3$ with finitely many concentric spherical $\delta$-shell interactions. The operators are defined by the quadratic form method and are described by continuity across each shell together with…
Quantum $A_2$-Toda field theory in two dimensions is investigated based on the method of quantizing canonical free field. Toda exponential operators associated with the fundamental weights are constructed to the fourth order in the…
Given an arbitrary sequence of elements $\xi=\{\xi_n\}_{n\in \mathbb{N}}$ of a Hilbert space $(\mathcal{H},\langle\cdot,\cdot\rangle)$, the operator $T_\xi$ is defined as the operator associated to the sesquilinear form $…
The definitions and some properties (e.g. the Wigner-Eckart theorem, the fusion procedure) of covariant and contravariant q-tensor operators for quasitriangular quantum Lie algebras are formulated in the R-matrix language. The case of…
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…
The notion of the genus of a quadratic form is generalized to vertex operator algebras. We define it as the modular braided tensor category associated to a suitable vertex operator algebra together with the central charge. Statements…
In this paper, we introduce a new differential-difference operator $T_\xi$ $(\xi \in \mathbb{R}^N)$ by using projections associated to orthogonal subsystems in root systems. Similarly to Dunkl theory, we show that these operators commute…
Centered weighted composition operators on $L^2$-spaces are characterized. The characterization is obtained without the assumption that the operator is a product of a multiplication and a composition operator. The concept of spectrally…