相关论文: Three Short Distance Structures from Quantum Algeb…

Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…

A new family of analytically solvable quantum geometric models is proposed. The structure of the energy spectra as well as the form of the corresponding eigenfunctions are presented pointing out their main specific properties.

It is shown that some operators in quantum mechanics have hidden structures that are unobservable in principle. These structures are based on a supersymmetric decomposition of the momentum operator, and a nonassociative decomposition of the…

A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.

The Kuchar observables notion is shown to apply only to a limited range of theories. Relational mechanics, slightly inhomogeneous cosmology and supergravity are used as examples that require further notions of observables. A suitably…

Within the unified framework of exploiting the relative entropy as a distance measure of quantum correlations, we make explicit the hierarchical structure of quantum coherence, quantum discord and quantum entanglement in multipartite…

We define coarse proximity structures, which are an analog of small-scale proximity spaces in the large-scale context. We show that metric spaces induce coarse proximity structures, and we construct a natural small-scale proximity…

We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display…

Quantum simulation is making a significant impact on scientific research. The prevailing tendency of the field is to build quantum simulators that get closer to real-world systems of interest, in particular electronic materials. However,…

We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…

Several lines of evidence suggest that quantum gravity at very short distances may behave effectively as a two-dimensional theory. I summarize these hints, and offer an additional argument based on the strong-coupling limit of the…

In this book super interval matrices using the special type of intervals of the form [0, a] are introduced. Several algebraic structures like semigroups, groups, semirings, rings, semivector spaces and vector spaces are introduced. Special…

We review the relationship between discrete groups of symmetries of Euclidean three-space, constructions in algebraic geometry around Kleinian singularities including versions of Hilbert and Quot schemes, and their relationship to…

We review briefly a stream of ideas concerning the role of quantum groups as hidden symmetries in conformal field theories, paying particular attention to the field theoretical representations of quantum groups based on Coulomb gas methods.…

In this paper, we present a collection of results on the observability of quantum mechanical systems, in the case the output is the result of a discrete nonselective measurement. By defining an effective observable we extend previous…

Quantum algebras (also called quantum groups) are deformed versions of the usual Lie algebras, to which they reduce when the deformation parameter q is set equal to unity. From the mathematical point of view they are Hopf algebras. Their…

We study functional analytic aspects of two types of correction terms to the Heisenberg algebra. One type is known to induce a finite lower bound $\Delta x_0$ to the resolution of distances, a short distance cutoff which is motivated from…

Homology theories for associative algebraic structures are well established and have been studied for a long time. More recently, homology theories for self-distributive algebraic structures motivated by knot theory, such as quandles and…

An exterior derivative, inner derivation, and Lie derivative are introduced on the quantum group $GL_{q}(N)$. $SL_{q}(N)$ is then found by constructing matrices with determinant unity, and the induced calculus is found.

Based on a recent purely geometric construction of observables for the spatial diffeomorphism constraint, we propose two distinct quantum reductions to spherical symmetry within full 3+1-dimensional loop quantum gravity. The construction of…