Related papers: Superoscillations and Fock spaces
We propose to describe bulk wave functions of fractional quantum Hall states in terms of correlators of non-unitary b/c-spin systems. These yield a promising conformal field theory analogon of the composite fermion picture of Jain.…
We revisit the non-perturbative renormalization of a class of simple polaron models with resting fermions. The considered dispersion relations and form factors are allowed to be highly singular, such that infinite self-energies and wave…
We explore conformal primary wavefunctions for all half integer spins up to the graviton. Half steps are related by supersymmetry, integer steps by the classical double copy. The main results are as follows: we 1) introduce a convenient…
The hamiltonian formulation of Supersymmetric Yang-Mills quantum mechanics (SYMQM) is discussed. We focus on the Fock space formulation of the models since it is convenient for the numerical analysis, however some novel analytical results…
We reinvestigate the Calogero-Sutherland-type (CS-type) models and generalized hypergeometric functions. We construct the generalized CS operators for circular, Hermite, Laguerre, Jacobi and Bessel cases and establish the generalized…
In this paper we continue to develop further our prescription [arXiv:1602.02962] to holographically compute the conformal partial waves of CFT correlation functions using the gravitational open Wilson network operators in the bulk. In…
Fractional supersymmetric quantum mechanics of order $\lambda$ is realized in terms of the generators of a generalized deformed oscillator algebra and a Z$_{\lambda}$-grading structure is imposed on the Fock space of the latter. This…
We further develop the concept of supergrowth [Jordan, Quantum Stud.: Math. Found. $\textbf{7}$, 285-292 (2020)], a phenomenon complementary to superoscillation, defined as the local amplitude growth rate of a function being higher than its…
We revisit the Fourier transform of a Hankel function, of considerable importance in the theory of knife edge diffraction. Our approach is based directly upon the underlying Bessel equation, which admits manipulation into an alternate…
It is well known that for every measurable function $a$, essentially bounded on the positive halfline, the corresponding radial Toeplitz operator $T_a$, acting in the Segal--Bargmann--Fock space, is diagonal with respect to the canonical…
The space of entire functions which are integrable with respect to the Gaussian weight, known also as the Fock space, is one of the preferred functional Hilbert spaces for modelling and experimenting harmonic analysis, quantum mechanics or…
Relativistic geometrical action for a quantum particle in the superspace is analyzed from theoretical group point of view. To this end an alternative technique of quantization outlined by the authors in a previous work and that is based in…
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…
We model generalized harmonic functions on rings of differential operators and complex function spaces. The differential operators in the second Weyl-algebra that commute with rotations are described and leads to a natural notion for such…
Usually in quantum mechanics the Heisenberg algebra is generated by operators of position and momentum. The algebra is then represented on an Hilbert space of square integrable functions. Alternatively one generates the Heisenberg algebra…
Wavelet-type random series representations of the well-known Fractional Brownian Motion (FBM) and many other related stochastic processes and fields have started to be introduced since more than two decades. Such representations provide…
We consider the nature of the wave function using the example of a harmonic oscillator. We show that the eigenfunctions $\psi_n{=}z^n$ of the quantum Hamiltonian in the complex Bargmann-Fock-Segal representation with $z\in\mathbb C$ are the…
We present a systematic study of the Rayleigh--Ritz variational method for quantum oscillators in the Segal--Bargmann space. We rigorously derive the normalizability condition $|\alpha| < \tfrac{1}{2}$ for generalized Gaussian trial…
We present a general diagrammatic approach to the construction of efficient algorithms for computing a Fourier transform on a semisimple algebra. This extends previous work wherein we derive best estimates for the computation of a Fourier…
A method for obtaining complex analytic realizations for a class of deformed algebras based on their respective deformation mappings and their ordinary coherent states is introduced. Explicit results of such realizations are provided for…