相关论文: Noncommutative extensions of the Fourier transform…
In this paper we study a family of commutative algebras generated by two infinite sets of generators. These algebras are parametrized by Young diagrams. We explain a connection of these algebras with the fusion product of integrable…
Form factors in planar $\mathcal{N}=4$ super-Yang-Mills theory have a dual description in terms of periodic Wilson loops. This duality maps the multi-collinear expansion of the former to an operator product expansion of the latter. The…
The machinery of noncommutative Schur functions provides a general tool for obtaining Schur expansions for combinatorially defined symmetric functions. We extend this approach to a wider class of symmetric functions, explore its strengths…
We define matrix models that converge to the generating functions of a wide variety of loop models with fugacity taken in sets with an accumulation point. The latter can also be seen as moments of a non-commutative law on a subfactor planar…
We consider non-selfadjoint operator algebras $\mathfrak{L}(G,\lambda)$ generated by weighted creation operators on the Fock-Hilbert spaces of countable directed graphs $G$. These algebras may be viewed as noncommutative generalizations of…
Quantum group Fourier transform methods are applied to the study of processes on noncommutative Minkowski spacetime $[x^i,t]=\imath\lambda x^i$. A natural wave equation is derived and the associated phenomena of {\it in vacuo} dispersion…
In this article we considered models of particles living in a three-dimensional space-time with a nonstandard noncommutativity induced by shifting canonical coordinates and momenta with generators of a unitary irreducible representation of…
In this paper, we explore Fourier analysis for noncommutative $L_p$ space-valued functions on $G$, where $G$ is a totally disconnected non-abelian compact group. By additionally assuming that the value of these functions remains invariant…
Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…
We define a new class of generating function transformations related to polylogarithm functions, Dirichlet series, and Euler sums. These transformations are given by an infinite sum over the $j^{th}$ derivatives of a sequence generating…
According to harmonic analysis (Fourier analysis), any function $f(x)$, periodic over the interval $[-L, L]$, which satisfies the Dirichlet conditions, can be developed into an infinite sum (known in the literature as the trigonometric…
We introduce a general class of generating functionals for the calculation of quantum-mechanical expectation values of arbitrary functionals of fluctuating paths with fixed end points in configuration or momentum space. The generating…
While Wigner functions forming phase space representation of quantum states is a well-known fact, their construction for noncommutative quantum mechanics (NCQM) remains relatively lesser known, in particular with respect to gauge…
A theorem of Siebert asserts that if a sequence of semigroups of probability measures on a Lie group G is weakly convergent to a semigroup of the same type, then the corresponding generating functionals are convergent in the weak operator…
We present a new approach to constructing unconditional pseudorandom generators against classes of functions that involve computing a linear function of the inputs. We give an explicit construction of a pseudorandom generator that fools the…
A novel generalization of the Askey-Wilson algebra is presented and shown to be associated with coproducts in the quantum algebra $U_q(su(1,1))$. This algebra has 15 non-commuting generators given by $Q^{(A)}$, with $A\subset \{1,2,3,4\}$…
In this paper, we provide a solution to the open problem of computing the Fourier transform of a binary function defined over $n$-bit vectors taking $m$-bit vector values. In particular, we introduce the two-modular Fourier transform (TMFT)…
The main goal is to interpret the Askey-Wilson function and the corresponding transform pair on the quantum SU(1,1) group. A weight on the C^*-algebra of continuous functions vanishing at infinity on the quantum SU(1,1) group is studied,…
We show that U(\infty) symmetry transformations of the noncommutative field theory in the Moyal space are generated by a combination of two W_{1+\infty} algebras in the Landau problem. Geometrical meaning of this infinite symmetry is…
In this paper we construct a noncommutative space of ``pointed Drinfeld modules'' that generalizes to the case of function fields the noncommutative spaces of commensurability classes of Q-lattices. It extends the usual moduli spaces of…