相关论文: Quantum sets and Gelfand spectra (Ortho-sets and G…

We consider some generalization of the theory of quantum states, which is based on the analysis of long standing problems and unsatisfactory situation with the possible interpretations of quantum mechanics. We demonstrate that the…

We introduce to this paper new kinds of coherent states for some quantum solvable models: a free particle on a sphere, one-dimensional Calogero-Sutherland model, the motion of spinless electrons subjected to a perpendicular magnetic field…

We review a notion of completeness in QFT arising from the analysis of basic properties of the set of operator algebras attached to regions. In words, this completeness asserts that the physical observable algebras produced by local degrees…

The formulation and resolution of integrable lattice statistical models in a quantum group covariant way is the subject of this review. The Bethe Ansatz turns to be remarkably useful to implement quantum group symmetries and to provide…

A concept -- quantum order -- is introduced to describe a new kind of orders that generally appear in quantum states at zero temperature. Quantum orders that characterize universality classes of quantum states (described by {\em complex}…

A major problem in the consistent-histories approach to quantum theory is contending with the potentially large number of consistent sets of history propositions. One possibility is to find a scheme in which a unique set is selected in some…

We construct the systems of generalised coherent states for the discrete and continuous spectra of the hydrogen atom. These systems are expressed in elementary functions and are invariant under the $SO(3, 2)$ (discrete spectrum) and $SO(4,…

In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…

The scientific methodology based on two descriptive levels, ontic (reality as it is ) and epistemic (observational), is briefly presented. Following Schr\"odinger, we point to the possible gap between these two descriptions. Our main aim is…

We give a derivation of quantum spectral curve (QSC) - a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4 SYM theory proposed in our recent paper Phys.Rev.Lett. 112 (2014). We also generalize this construction to all…

A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…

We describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S^d. The coherent states are labeled by points in the associated…

The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…

Inspired by classical ("actual") Quantum Theory over $\mathbb{C}$ and Modal Quantum Theory (MQT), which is a model of Quantum Theory over certain finite fields, we introduce General Quantum Theory as a Quantum Theory -- in the K{\o}benhavn…

P-algebras are a non-commutative, non-associative generalization of Boolean algebras that are for quantum logic what Boolean algebras are for classical logic. P-algebras have type <X, 0, ', .> where 0 is a constant, ' is unary and . is…

Quantum superpositions of coherent states are produced both in microwave and optical domains, and are considered realizations of the famous "Schr\"odinger cat" state. The recent progress shows an increase in the number of components and the…

Two important classes of quantum structures, namely orthomodular posets and orthomodular lattices, can be characterized in a classical context, using notions like partial information and points of view. Using the formalism of representation…

Atomic-like systems in which electronic motion is two dimensional are now realizable as ``quantum dots''. In place of the attraction of a nucleus there is a confining potential, usually assumed to be quadratic. Additionally, a perpendicular…

A composite quantum system has properties that are incompatible with every property of its parts. The existence of such global properties incompatible with all local properties constitutes what I call "mereological holism"--the distinctive…

Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…