Related papers: Quantum Mechanics of Extended Objects
The present paper shows how one might model Everettian quantum mechanics using hyperfinitely many worlds. A hyperfinite model allows one to consider idealized measurements of observables with continuous-valued spectra where different…
The continuous quantum measurement within the probability representation of quantum mechanics is discussed. The partial classical propagator of the symplectic tomogram associated to a particular measurement outcome is introduced, for which…
We elaborate on a geometric characterization of the electromagnetic properties of matter. A fundamental complex quantity, z_{L}, is introduced to study the localization properties of extended quantum systems. z_L, which allows us to…
Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only…
The development of the new logic of partitions (= equivalence relations) dual to the usual Boolean logic of subsets, and its quantitative version as the new logical theory of information provide the basic mathematical concepts to describe…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
The quantum Liouville equation, which describes the phase space dynamics of a quantum system of fermions, is analyzed from statistical point of view as a particular example of the Kramers-Moyal expansion. Quantum mechanics is extended to…
The suggested theory is the new quantum mechanics (QM) interpretation.The research proves that QM represents the electrodynamics of the curvilinear closed (non-linear) waves. It is entirely according to the modern interpretation and…
A resolution of the quantum measurement problem(s) using the consistent histories interpretation yields in a rather natural way a restriction on what an observer can know about a quantum system, one that is also consistent with some results…
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…
We quantise complex, infinite-dimensional projective space CP(H). We apply the result to quantise a complex, finite-dimensional, classical phase space C whose symplectic volume is infinite, by holomorphically embedding it into CP(H). The…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
A rather non-standard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation has gained some attention in recent years, due to its possible relation with Planck scale…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
This paper develops a deterministic model of quantum mechanics as an accumulation-and-threshold process. The model arises from an analogy with signal processing in wireless communications. Complex wavefunctions are interpreted as expressing…
In this paper, we discuss a geometrodynamical approach to particle physics, in which quantum mechanics is no more than an approximated model of nature in the microscopic scale. We derive quantum mechanics from the concept of non-local…