Related papers: Quantum Observables and a Model of Noncommutativit…
The author's attempt to construct a local causal model of quantum theory (QT) that includes quantum field theory (QFT) resulted in the identification of "quantum objects" as the elementary units of causality and locality. Quantum objects…
Noncommutativity of observables is a central feature of quantum physics. It plays a fundamental role in the formulation of the uncertainty principle for complementary variables and strongly affects the laws of thermodynamics for systems…
We describe a scheme of quantum mechanics in which the Hilbert space and linear operators are only secondary structures of the theory. As primary structures we consider observables, elements of noncommutative algebra, and the physical…
Application of the noncommutative geometry to several physical models is considered.
In the Contextuality-by-Default theory random variables representing measurement outcomes are labeled contextually, i.e., not only by what they measure but also under what conditions (in what contexts) the measurements are made, including…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
Given two or more non-commuting observables, it is generally not possible to simultaneously assign precise values to each. This quantum mechanical uncertainty principle is widely understood to be encapsulated by some form of uncertainty…
In the work it is shown that the principles "the objective local theory" and corollaries of the standard quantum mechanics are not in such antagonistic inconsistency as it is usually supposed. In the framework of algebraic approach, the…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
Quantum field planes furnish a noncommutative differential algebra $\Omega$ which substitutes for the commutative algebra of functions and forms on a contractible manifold. The data required in their construction come from a quantum field…
Quantum circuits -- built from local unitary gates and local measurements -- are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far-from-equilibrium. These models have shed…
We show that the linearity of an evolution of Quantum Mechanics follows from the definition of kinematics. The same result is obtained for an arbitrary theory with the state space that includes mixtures of different preparations. Next, we…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
In this work, I investigate the noncommutative Poisson algebra of classical observables corresponding to a proposed general Noncommutative Quantum Mechanics, \cite{1}. I treat some classical systems with various potentials and some Physical…
We develop the general quantum stochastic approach to the description of quantum measurements continuous in time. The framework, that we introduce, encompasses the various particular models for continuous-time measurements condsidered…
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.
A soluble model for the relativistically description of an unstable system is given in terms of relativistic quantum field theory, with a structure similar to Van Hove's generalization of the Lee model in the non-relativistic theory.
In this work we present a re-evaluation of the concept of time in non-relativistic quantum theory. We suggest a formalism in which time is changed into the status of an operator, and where expectation values of observables and the state of…