Related papers: Fock representation of free convolution powers
In this paper we study the Fock representation of a certain $*$-algebra which appears naturally in the framework of quantum group theory. It is also a generalization of the twisted CCR-algebra introduced by W. Pusz and S.~Woronowicz. We…
The angular coefficients $\psi_{k,p}(\alpha,\theta)$ of the Fock expansion characterizing the S-state wave function of the two-electron atomic system, are calculated in hyperspherical angular coordinates $\alpha$ and $\theta$. To solve the…
There are quantum states of light that can be expressed as finite superpositions of Fock states (FSFS). We demonstrate the nonclassicality of an arbitrary FSFS by means of its phase space distributions such as the Wigner function and the…
We give the Fock representation of a noncommutative $\mathbb{C}P^N$ and gauge theories on it. The Fock representation is constructed based on star products given by deformation quantization with separation of variables and operators which…
The Grothendieck groups of the categories of finitely generated modules and finitely generated projective modules over a tower of algebras can be endowed with (co)algebra structures that, in many cases of interest, give rise to a dual pair…
Invariant creation and annihilation operators and related Fock states and coherent states are built up for the system of nonstationary fermionic forced oscillator.
The notion of the eigenvalue problem in the Fock space with polynomial eigenfunctions is introduced. This problem is classified by using the finite-dimensional representations of the $\mathfrak{sl}(2)$-algebra in Fock space. In the complex…
A Fock representation of the quantum affine algebra $U_q(\widehat{\sl}_2)$ is constructed by three bosonic fields for an arbitrary level with the help of the Drinfeld realization.
We generalize several results on Toeplitz operators over reflexive, standard weighted Fock spaces $F_t^p$ to the non-reflexive cases $p = 1, \infty$. Among these results are the characterization of compactness and the Fredholm property of…
We define an extension of the polynomial calculus on a W*-probability space by introducing an abstract algebra which contains polynomials. This extension allows us to define transition operators for additive and multiplicative free…
We construct a quantum field theory in noncommutative spacetime by twisting the algebra of quantum operators (especially, creation and annihilation operators) of the corresponding quantum field theory in commutative spacetime. The twisted…
Utilizing Lie superalgebra (LS) realizations via the Relative Parabose Set algebra $P_{BF}$, combined with earlier results on the Fock-like representations of $P_{BF}^{(1,1)}$, we proceed to the construction of a family of Fock-like…
We establish a central limit theorem for the sum of $\epsilon$-independent random variables, extending both the classical and free probability setting. Central to our approach is the use of graphon limits to characterize the limiting…
Noncommutative multivariable versions of weighted shifts arise naturally as `weighted' left creation operators acting on Fock space. We investigate the unital weak operator topology closed algebras they generate. The unweighted case yields…
The Fock expansion, which describes the properties of two-electron atoms near the nucleus, is studied. The angular Fock coefficients $\psi_{k,p}(\alpha,\theta)$ with the maximum possible value of subscript $p$ are calculated on examples of…
The earlier treatments of Lorentz covariant harmonic oscillator have brought to light various difficulties, such as reconciling Lorentz symmetry with the full Fock space, and divergence issues with their functional representations. We…
We introduce a twisted version of the Heisenberg double, constructed from a twisted Hopf algebra and a twisted Hopf pairing. We state a Stone--von Neumann type theorem for a natural Fock space representation of this twisted Heisenberg…
We study the distribution (w.r.t. the vacuum state) of family of partial sums Sm of position operators on weakly monotone Fock space. We show that any single operator has the Wigner law, and an arbitrary family of them (with the index set…
A cosmographic reconstruction of $f(\mathcal T)$ models is here revised in a model independent way by fixing observational bounds on the most relevant terms of the $f(\mathcal T)$ Taylor expansion. We relate the $f(\mathcal T)$ models and…
We describe a background independent quantization of the scalar field that provides an explicit realization of Fock-like states and associated operators in a polymer Hilbert space. The vacuum expectation values of the commutator and…