Related papers: $SO(3)$-Berezin-Toeplitz quantization and the AJ c…
In this note we quantize the free $ * $-algebra generated by finitely many variables, which is a new example of the theory of Toeplitz quantization of $ * $-algebras as developed previously by the author. This is achieved by defining…
Monopole operators in Abelian N=4 Chern-Simons theories described by circular quiver diagrams are investigated. The magnetic charges of non-diagonal U(1) gauge symmetries form the SU(p)xSU(q) root lattice where p and q are numbers of…
Using geometric quantization, we represent curve operators in the TQFT of Witten-Reshetikhin-Turaev with jauge group SU_2 as Toeplitz operators with symbols corresponding to trace functions. As an application, we show that eigenvectors of…
Using the approach based on sesquilinear forms, we introduce Toeplitz operator in the analytic Bergman space on the upper half-plane with strongly singular symbols, derivatives of measures. Conditions for boundedness and compactness of such…
We consider the weighted Bergman spaces HL^2(B^d,\mu_{\lambda}), where d\mu_\lambda(z)=c_{\lambda}(1-|z|^2)^lambda d\tau, \tau being the hyperbolic volume measure. These spaces are nonzero if and only if \lambda>d. For 0<\lambda\leq d,…
In a series of papers on Bohr-Sommerfeld-Heisenberg quantization of completely integrable systems we interpreted shifting operators as quantization of functions ${\mathrm{e}}^{ \pm i{\theta}_j}$ , where $(I_j , {\theta}_j )$ are action…
We show that Brennan's conjecture is equivalent to boundedness of composition operators on homogeneous Sobolev spaces generated by conformal homeomorphisms of simply connected plane domains to the unit disc.
A simple geometric way is suggested to derive the Ward identities in the Chern-Simons theory, also known as quantum $A$- and $C$-polynomials for knots. In quasi-classical limit it is closely related to the well publicized augmentation…
The parity operator for a parity-symmetric quantum field theory transforms as an infinite sum of irreducible representations of the homogeneous Lorentz group. These representations are connected with Wilson polynomials.
We consider N = 3 supersymmetric Chern-Simons gauge theories with product unitary and orthosymplectic groups and bifundamental and fundamental fields. We study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov matrix…
By the quantization condition compact quantizable Kaehler manifolds can be embedded into projective space. In this way they become projective varieties. The quantum Hilbert space of the Berezin-Toeplitz quantization (and of the geometric…
We study Toeplitz operators with uniformly continuous symbols on generalized harmonic Bergman spaces of the unit ball in $\mathbb{R}^n$. We describe their essential spectra and establish a short exact sequence associated with the…
The annihilation operators on Bernoulli functionals (Bernoulli annihilators, for short) and their adjoint operators satisfy a canonical anti-commutation relation (CAR) in equal-time. As a mathematical structure, Dirichlet forms play an…
Recent results on zero modes of the Abelian Dirac operator in three dimensions support to some degree the conjecture that the Chern-Simons action admits only certain quantized values for gauge fields that lead to zero modes of the…
We prove a Jensen-disc type theorem for polynomials $p\in\mathbb{R}[z]$ having all their zeros in a sector of the complex plane. This result is then used to prove the existence of a collection of linear operators…
In this note, we summarize recent progress in constructing and then semi-classically quantizing solitons, or non-abelian Q-balls, in the symmetric space sine-Gordon theories. We then consider the images of these solitons in the related…
This paper is devoted to semi-classical aspects of symplectic reduction. Consider a compact prequantizable Kahler manifold M with a Hamiltonian torus action. Guillemin and Sternberg introduced an isomorphism between the invariant part of…
We present a new expression for the partition function of refined Chern-Simons theory on $S^3$ with arbitrary gauge group, which is explicitly equal to $1$, when the coupling constant is zero. Using this form of partition function we show…
In this paper we prove that if S equals a finite sum of finite products of Toeplitz operators on the Bergman space of the unit disk, then S is compact if and only if the Berezin transform of S equals 0 on the boundary of the disk. This…
A general class of W-algebras can be constructed from the affine sl(N) algebra by (quantum) Drinfeld-Sokolov reduction and are classified by partitions of N. Surface operators in an N=2 SU(N) 4d gauge theory are also classified by…