Related papers: Quantum surfaces, special functions, and the tunne…

We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision making) - quantum-like modeling. Projective measurements describe the canonical measurements of the basic…

First steps are taken in a project to construct a general class of conformal and perhaps, eventually, non-conformal quantum field theories of (n-1)-dimensional extended objects in a d=2n dimensional conformal space-time manifold M. The…

An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended to complex manifolds.…

This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…

It is shown with the help of skew-symmetric forms that the mathematical physics equations, on which no additional conditions are imposed, have quantum properties. And this is due to the integrability properties of differential equations,…

A growing number of studies is being devoted to the identification of plausible quantum properties of spacetime which might give rise to observably large effects. The literature on this subject is now relatively large, including studies in…

We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…

We study a class of algebras with non-Lie commutation relations whose symplectic leaves are surfaces of revolution: a cylinder or a torus. Over each of such surfaces we introduce a family of complex structures and Hilbert spaces of…

"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…

We present results relevant to the relation between quantum effects in a Riemannian space and on the surface appearing as a result of its isometric embedding in a flat space of a higher dimension. We discuss the mapping between the Hawking…

The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…

Electronic properties of quantum materials solids are often well understood via the low energy dispersion of Bloch bands, motivating single band approximations in many metals and semiconductors. However, a closer look reveals length and…

We present a mathematical framework for quantum mechanics in which the basic entities and operations have physical significance. In this framework the primitive concepts are states and effects and the resulting mathematical structure is a…

We clearly refine the fundamental framework of the thin-layer quantization procedure, and further develop the procedure by taking the proper terms of degree one in $q_3$ ($q_3$ denotes the curvilinear coordinate variable perpendicular to…

Sums play a prominent role in the formalisms of quantum mechanics, be it for mixing and superposing states, or for composing state spaces. Surprisingly, a conceptual analysis of quantum measurement seems to suggest that quantum mechanics…

Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…

We construct two-dimensional non-commutative topological quantum field theories (TQFTs), one for each Hecke algebra corresponding to a finite Coxeter system. These TQFTs associate an invariant to each ciliated surface, which is a Laurent…

We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the…

The basic framework for a systematic construction of a quantum theory of Riemannian geometry was introduced recently. The quantum versions of Riemannian structures --such as triad and area operators-- exhibit a non-commutativity. At first…

By the universal integrability objects we mean certain monodromy-type and transfer-type operators, where the representation in the auxiliary space is properly fixed, while the representation in the quantum space is not. This notion is…