Related papers: Quantale Modules and their Operators, with Applica…

The space, on which quantum field operators are given, is constructed in any theory, in which the usual product between test functions is substituted by the $\star$-product (the Moyal-type product). The important example of such a theory is…

In this paper the concept of Q-fuzzification of ideals of gamma-semigroups has been introduced and some important properties have been investigated. A characterization of regular gamma-semigroup in terms of Q-fuzzy ideals has been obtained.…

Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space…

This work deals with function theory on quantum complex hyperbolic spaces. The principal notions are expounded. We obtain explicit formulas for invariant integrals on `finite' functions on a quantum hyperbolic space and on the associated…

We describe quantizations on monoidal categories of modules over finite groups. They are given by quantizers which are elements of a group algebra. Over the complex numbers we find these explicitly. For modules over S3 and A4 we are given…

Quantum mechanics of models is considered which are constructed in spaces with Lie algebra type commutation relations between spatial coordinates. The case is specialized to that of the group SU(2), for which the formulation of the problem…

Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…

In this paper we study modular tensor categories (braided rigid balanced tensor categories with additional finiteness and non-degeneracy conditions), in particular, representations of quantum groups at roots of unity. We show that the…

This paper deals with quon algebras or deformed oscillator algebras, for which the deformation parameter is a root of unity. We show the interest of such algebras for fractional supersymmetric quantum mechanics, angular momentum theory and…

Faster algorithms, novel cryptographic mechanisms, and alternative methods of communication become possible when the model underlying information and computation changes from a classical mechanical model to a quantum mechanical one. Quantum…

Let $R$ be an associative ring with identity. This paper investigates the structure of the monomorphism category of large $R$-modules and establishes connections with the category of contravariant functors defined on finitely presented…

We develop a theory of holomorphic functions in several noncommuting (free) variables and thus provide a framework for the study of arbitrary n-tuples of operators. The main topics are the following: Free holomorphic functions and Hausdorff…

The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…

Ultracold molecules confined in optical lattices or tweezer traps can be used to process quantum information and simulate the behaviour of many-body quantum systems. Molecules offer several advantages for these applications. They have a…

In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…

This is the second part in a series of papers presenting a theory of tensor products for module categories for a vertex operator algebra. In Part I (hep-th/9309076), the notions of $P(z)$- and $Q(z)$-tensor product of two modules for a…

This paper provides an extensive study of the homotopy theory of types of algebras with units, like unital associative algebras or unital commutative algebras for instance. To this purpose, we endow the Koszul dual category of curved…

This research extends quantum singular value transformation (QSVT) for general bounded operators embedded in unitary operators on possibly infinite-dimensional Hilbert spaces. Through in-depth mathematical exploration, we have achieved a…

In [11] the authors investigated a family of quotient Hilbert modules in the Cowen-Douglas class over the unit disk constructed from classical Hilbert modules such as the Hardy and Bergman modules. In this paper we extend the results to the…

We present a theory of "quantum references", similar to lenses in classical functional programming, that allow to point to a subsystem of a larger quantum system, and to mutate/measure that part. Mutable classical variables, quantum…