Related papers: Finite-Dimensional Convex Effect Algebras
In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…
The application of principles of Quantum Mechanics in areas outside of physics has been getting increasing attention in the scientific community in an emergent discipline called Quantum Cognition. These principles have been applied to…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are obtained through sequential probing of quantum systems; no presuppositions…
We study general nilpotent algebras. The results obtained are new even for the classical algebras, such as associative or Lie algebras. We single out certain generic properties of finite-dimensional algebras, mostly over infinite fields.…
We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which is connected not necessarily with partially ordered groups, but rather with generalized pseudo effect algebras where the greatest element is not…
In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the…
We study optical spectra of finite electronic quantum systems at frequencies smaller than the plasma frequency using a quasi-classical approach. This approach includes collective effects and enables us to analyze how the nature of the…
We apply the notion of a full convex subcategory to a wide range of algebras including tilted, quasi-tilted, shod, weakly shod, left and right glued, laura, simply connected, strongly simply connected, left supported, and cluster-tilted. In…
In this paper we start with the development of a theory of presheaves on a lattice, in particular on the quantum lattice $\LL(\kH)$ of closed subspaces of a complex Hilbert space $\kH$, and their associated etale spaces. Even in this early…
Vertex algebras in higher dimensions correspond to models of quantum field theory with global conformal invariance. Any vertex algebra in dimension D admits a restriction to a vertex algebra in any lower dimension and, in particular, to…
In the context of Covariant Quantum Mechanics for a spin particle, we classify the ``quantum vector fields'', i.e. the projectable Hermitian vector fields of a complex bundle of complex dimension 2 over spacetime. Indeed, we prove that the…
Using very simple arguments we show that the quantum effects of an ultra-light particle as the Scalar Field Dark Matter $m_{SFDM}\sim10^{-22}$eV cannot be neglected at classical scales. We show that the effective density of this effect is…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
We consider the functions in two variables on an arbitrary poset, for which the convolution operation is defined. We obtain the generalization of incidence algebra and describe its properties: invertibility, the Jackobson radical,…
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
This is a graduate-level introduction to C*-algebras, Hilbert C*-modules, vector bundles, and induced representations of groups and C*-algebras, with applications to quantization theory, phase space localization, and configuration space…
State operators on convex effect algebras, in particular effect algebras of unital JC-algebras, JW-algebras and convex sigma-MV algebras are studied and their relations with conditional expectations in algebraic sense as well as in the…
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…
The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…