Related papers: A Generalized Quantum Theory
Having started with the general formulation of the quantum theory of the real scalar field (QFT) in the general Riemannian space--time $ V_{1,3} $, the general--covariant quasinonrelativistic quantum mechanics of a point-like spinless…
Standard quantum mechanics unquestionably violates the separability principle that classical physics (be it point-like analytic, statistical, or field-theoretic) accustomed us to consider as valid. In this paper, quantum nonseparability is…
An interesting link between two very different physical aspects of quantum mechanics is revealed; these are the absence of third-order interference and Tsirelson's bound for the nonlocal correlations. Considering multiple-slit experiments -…
In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which is an algebra generated by…
Linear spaces with an Euclidean metric are ubiquitous in mathematics, arising both from quadratic forms and inner products. Operators on such spaces also occur naturally. In recent years, the study of multivariate operator theory has made…
We extend significantly previous works on the Hilbert space representations of the Generalized Uncertainty Principle (GUP) in 3+1 dimensions of the form $[X_i,P_j] = i F_{ij}$ where $ F_{ij} = f(P^2) \delta_{ij} + g(P^2) P_i P_j $ for any…
Quantum theory does not provide a unique definition for the joint probability of two non-commuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
Quantum-mechanical observables for spatial and spacetime localization are considered from a lattice-theoretic perspective. It is shown that when replacing the lattice of all complex orthogonal projections underlying the Born rule by the…
A conceptual variable is any variable defined by a person or by a group of persons. Such variables may be inaccessible, meaning that they cannot be measured with arbitrary accuracy on the physical system under consideration at any given…
Until recently, a quantum instrument was defined to be a completely positive operation-valued measure from the set of states on a Hilbert space to itself. In the last few years, this definition has been generalized to such measures between…
The standard postulates of quantum theory can be divided into two groups: the first one characterizes the structure and dynamics of pure states, while the second one specifies the structure of measurements and the corresponding…
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
We discuss certain generalization of the Hilbert space of states in noncommutaive quantum mechanics that, as we show, introduces magnetic monopoles into the theory. Such generalization arises very naturally in the considered model, but can…
We constructed a Hilbert space representation of a contextual Kolmogorov model. This representation is based on two fundamental observables -- in the standard quantum model these are position and momentum observables. This representation…
So far, none of attempts to quantize gravity has led to a satisfactory model that not only describe gravity in the realm of a quantum world, but also its relation to elementary particles and other fundamental forces. Here, we outline the…
A quantum state can be understood in a loose sense as a map that assigns a value to every observable. Formalizing this characterization of states in terms of generalized probability distributions on the set of effects, we obtain a simple…
According to the Kolmogorovian Censorship Hypothesis, everything that quantum theory says about the world in the language of the quantum mechanical Hilbert space formalism is actually about relationships between ordinary relative…