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In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and describe some constructions of them. Then we study the formal distribution (noncommutative) Poisson algebras and coefficient (noncommutative)…
We survey some of the main conceptual developments in the study of PT-symmetric and pseudo-Hermitian Hamiltonian operators that have taken place during the past ten years or so. We offer a precise mathematical description of a quantum…
Recently, we introduced a mathematical framework for the quantization of a particle in a variable magnetic field. It consists in a modified form of the Weyl pseudodifferential calculus and a C*-algebraic setting, these two points of view…
Systems of neutral interacting mesons are investigated, concerning in particular the validity of their description by an effective hamiltonian. First, I study its connection to quantum field theory and show that the spectrum of such systems…
Operator systems are the unital self-adjoint subspaces of the bounded operators on a Hilbert space. Complex operator systems are an important category containing the C*-algebras and von Neumann algebras, which is increasingly of interest in…
It is known that holomorphic Poisson structures are closely related to theories of generalized K\"{a}hler geometry and bi-Hermitian structures. In this article, we introduce quantization of holomorphic Poisson structures which are closely…
We first review the introduction of star products in connection with deformations of Poisson brackets and the various cohomologies that are related to them. Then we concentrate on what we have called ``closed star products" and their…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of…
The treatment of high-dimensional problems such as the Schr\"odinger equation can be approached by concepts of tensor product approximation. We present general techniques that can be used for the treatment of high-dimensional optimization…
We show that several known results about the algebraic K-theory of tensor products of algebras with the C*-algebra of compact operators in Hilbert space remain valid for tensor products with any properly infinite C*-algebra.
As is known, there exists an alternative, "non-matricial" way to present basic notions and results of quantum functional analysis (= operator space theory). This approach is based on considering, instead of matrix spaces, a single space,…
Nambu's construction of multi-linear brackets for super-integrable systems can be thought of as degenerate Poisson brackets with a maximal set of Casimirs in their kernel. By introducing privileged coordinates in phase space these…
We study deformation quantization on an infinite-dimensional Hilbert space $W$ endowed with its canonical Poisson structure. The standard example of the Moyal star-product is made explicit and it is shown that it is well defined on a…
We devise a method based on the tensor-network formalism to calculate genuine multisite entanglement in ground states of infinite spin chains containing spin-1/2 or spin-1 quantum particles. The ground state is obtained by employing an…
We construct a new operation among representations of the symmetric group that interpolates between the classical internal and external products, which are defined in terms of tensor product and induction of representations. Following…
Starting with the well-defined product of quantum fields at two spacetime points, we explore an associated Poisson structure for classical field theories within the deformation quantization formalism. We realize that the induced…
We develop a complete theory of non-formal deformation quantization exhibiting a nonzero minimal uncertainty in position. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on…
The investigation of the behavior of both classical and quantum systems on non-Euclidean surfaces near the phase transition point represents an interesting research area of modern physics. In the case of classical spin systems, a…
We consider the Einstein deformations of the reducible rank two symmetric spaces of noncompact type. If $M$ is the product of any two real, complex, quaternionic or octonionic hyperbolic spaces, we prove that the family of nearby Einstein…