Related papers: Extended Voros product in the coherent states fram…
The deformation quantization of Moyal-Weyl star product of functions of quaternions is investigated.
We extend several relative perturbation bounds to Hermitian matrices that are possibly singular, and also develop a general class of relative bounds for Hermitian matrices. As a result, corresponding relative bounds for singular values of…
We compute the braided groups and braided matrices $B(R)$ for the solution $R$ of the Yang-Baxter equation associated to the quantum Heisenberg group. We also show that a particular extension of the quantum Heisenberg group is dual to the…
We study stability of amalgamated free products and HNN extensions of stable groups over finite groups. We focus on operator norm stability, Hilbert-Schmidt stability and stability in permutations. We provide many new examples of stable (or…
Vector coherent states (VCS) viewed as a generalization of ordinary coherent states for higher rank tensor Hilbert spaces are investigated. We consider a systematic way of generating classes of VCS which are solvable (i.e., in the present…
The variety of uniform matrix product states arises both in algebraic geometry as a natural generalization of the Veronese variety, and in quantum many-body physics as a model for a translation-invariant system of sites placed on a ring.…
We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…
A normal form transformation is carried out on the operators of a complete set of commuting observables in a multidimensional, integrable quantum system, mapping them by unitary conjugation into functions of the harmonic oscillators in the…
The main characteristics of the quantum oscillator coherent states including the two-particle Calogero interaction are investigated. We show that these Calogero coherent states are the eigenstates of the second-order differential…
We introduce the notion of homotopy inner products for any cyclic quadratic Koszul operad $\mathcal O$, generalizing the construction already known for the associative operad. This is done by defining a colored operad $\widehat{\mathcal…
The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The…
We study the rate of convergence for (variational) eigenvalues of several non-linear problems involving oscillating weights and subject to different kinds of boundary conditions in bounded domains.
We show that finite-dimensional order unit spaces equipped with a continuous sequential product as defined by Gudder and Greechie are homogeneous and self-dual. As a consequence of the Koecher-Vinberg theorem these spaces therefore…
In this paper the structures of the generalised Euler-Lagrange equations and their associated conserved quantities are derived for one-dimensional Herglotz variational problems of order $n$. Their derivations use the framework of moving…
For certain nilpotent real Lie groups constructed as semidirect products, algebras of invariant differential operators on some coadjoint orbits are used in the study of boundedness properties of the Weyl-Pedersen calculus of their…
Motivated by the recent developments of gauge-covariant methods in the phase-space, a systematic method is presented aiming at the generalisation of the Moyal star-product to a non-Abelian gauge covariant one at any order. Such an expansion…
Let $\mathfrak{g}$ be a Leibniz algebra and $E$ a vector space containing $\mathfrak{g}$ as a subspace. All Leibniz algebra structures on $E$ containing $\mathfrak{g}$ as a subalgebra are explicitly described and classified by two…
A duality property for star products is exhibited. In view of it, known star-product schemes, like the Weyl-Wigner-Moyal formalism, the Husimi and the Glauber-Sudarshan maps are revisited and their dual partners elucidated. The tomographic…
In this work we investigate discrete structures in product Hilbert spaces. For monopartite systems of size $d$ one relies on the Weyl-Heisenberg group $WH(d)$, while in the case of composite Hilbert spaces we identify designs covariant with…
The theory of alpha_star-cohomology is studied thoroughly and it is shown that in each cohomology class there exists a unique 2-cocycle, the harmonic form, which generates a particular Groenewold-Moyal star product. This leads to an…