Related papers: Weighted Catalan convolution and $(q,2)$-Fock spac…
We investigate numerical solution of $Q^2$ evolution equations for structure functions in the nucleon and in nuclei. (Dokshitzer-Gribov-Lipatov-)Altarelli-Parisi and Mueller-Qiu evolution equations are solved in a brute-force method.…
We introduce a class of sequences, defined by means of partial Bell polynomials, that contains a basis for the space of linear recurrence sequences with constant coefficients as well as other well-known sequences like Catalan and Motzkin.…
Let $\phi(z)=(\phi_1(z),...,\phi_n(z))$ be a holomorphic self-map of $B$ and $\psi(z)$ a holomorphic function on $B$, where $B$ is the unit ball of ${\Bbbb C}^n$. Let $0<p,s<+\infty, -n-1<q<+\infty, q+s>-1$ and $\alpha\geq 0,$ this paper…
We extend the graphical calculus developed in the first part of this paper to the parametrising spaces of quantum vertex operators. This involves a graphical implementation of the dynamical twist functor, which is a strict monoidal functor…
The structure positive of unitary irreducible representations of the noncompact $u_q(2,1)$ quantum algebra that are related to a positive discrete series is examined. With the aid of projection operators for the $su_q(2)$ subalgebra, a…
This paper examines the recursive sequence of polynomials $p_n(x)$, defined by $p_0(x) = x^2 - 2$ and $p_n(x) = p_{n-1}(x)^2 - 2$ for $n \geq 1$. It describes the field-theoretic motivations behind this sequence, derives a recursive formula…
We perform a perturbative QCD analysis of the nucleon's Pauli form factor $F_2(Q^2)$ in the asymptotically large $Q^2$ limit. We find that the leading contribution to $F_2(Q^2)$ has a $1/Q^6$ power behavior, consistent with the well-known…
A new class of alternating convolutions concerning binomial coefficients and Catalan numbers are evaluated in closed forms.
We find classes of driven conformal field theories (CFT) in d + 1 dimensions with d > 1, whose quench and Floquet dynamics can be computed exactly. The setup is suitable for studying periodic drives, consisting of square pulse protocols for…
We investigate the effects of the presence of conserved charges on the momentum-space entanglement of Quantum Field Theories (QFTs). We show that if a given model has superselection sectors, then it allows for different notions of momentum…
We analyze the proton electromagnetic form factor ratio $R(Q^{2})=QF_2(Q^{2})/F_1(Q^{2})$ as a function of momentum transfer $Q^{2}$ within perturbative QCD. We find that the prediction for $R(Q^{2})$ at large momentum transfer $Q$ depends…
Dynamics has been generalized to a noncommutative phase space. The noncommuting phase space is taken to be invariant under the quantum group $GL_{q,p}(2)$. The $q$-deformed differential calculus on the phase space is formulated and using…
For the case of spin zero we construct conjugate pairs of operators on Fock space. On states multiplied by polarization vectors coordinate operators Q conjugate to the momentum operator P exist. The massive case is derived from a…
The symplectic geometry of the phase space associated with a charged particle is determined by the addition of the Faraday 2-form to the standard structure on the Euclidean phase space. In this paper we describe the corresponding algebra of…
We construct a qubit algebra from field creation and annihilation operators acting on a global vacuum state. Particles to be used as qubits are created from the vacuum by a near-deterministic single particle source. Our formulation makes…
We obtain criteria for the boundedness and compactness of weighted composition operators between different Fock spaces in $\mathbb{C}^n$. We also give estimates for essential norm of these operators.
Following Kottler, \'E.Cartan, and van Dantzig, we formulate the Maxwell equations in a metric independent form in terms of the field strength $F=(E,B)$ and the excitation $H=({\cal D}, {\cal H})$. We assume a linear constitutive law…
In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
We demonstrate that dynamical noncommutative space-time will give rise to deformed oscillator algebras. In turn, starting from some q-deformations of these algebras in a two dimensional space for which the entire deformed Fock space can be…