Related papers: Quantum Hexaspherical Observables for Electrons
We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical…
Extra dimensions are introduced: 3 in Classical Mechanics and 6 in Relativistic Mechanics, which represent orientations, resulting from rotations, of a particle, described by quaternions, and leading to a 7-dimensional, respectively…
A simple model of quantum particle is proposed in which the particle in a {\it macroscopic} rest frame is represented by a {\it microscopic d}-dimensional oscillator, {\it s=(d-1)/2} being the spin of the particle. The state vectors are…
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
Despite conventional wisdom that spin-1/2 systems have no classical analog, we introduce a set of classical coupled oscillators with solutions that exactly map onto the dynamics of an unmeasured electron spin state in an arbitrary,…
Theoretical approaches to one-dimensional and quasi-one-dimensional quantum rings with a few electrons are reviewed. Discrete Hubbard-type models and continuum models are shown to give similar results governed by the special features of the…
We show that the isotropic harmonic oscillator in the ordinary euclidean space ${\bf R}^N$ ($N\ge 3$) admits a natural q-deformation into a new quantum mechanical model having a q-deformed symmetry (in the sense of quantum groups),…
A rigorous (and simple) proof is given that there is a one-to-one correspondence between causal anti-deSitter covariant quantum field theories on anti-deSitter space and causal conformally covariant quantum field theories on its conformal…
The appearance of tracks, close to classical orbits, left by charged quantum particles propagating inside a detector, such as a cavity periodically illuminated by light pulses, is studied for a family of idealized models. In the…
The review paper presents generalization of d'Alembert's variational principle: the dynamics of a quantum system for an external observer is defined by the exact equilibrium of all acting in the system forces, including the random quantum…
We present an operational reconstruction of the well-known two-to-one homomorphism between the groups $SU(2)$ and $SO(3)$, grounded in the physical description of quantum state preparation and evolution. Starting from the connection between…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
We develop a semiclassical framework for studying quantum particles constrained to curved surfaces using the momentous quantum mechanics formalism, which extends classical phase-space to include quantum fluctuation variables (moments). In a…
The motion of a conducting electron in a quantum dot with one or several dislocations in the underlying crystal lattice is considered in the continuum picture, where dislocations are represented by torsion of space. The possible effects of…
We extend the concept of Anderson localization, the confinement of quantum information in a spatially irregular potential, to quantum circuits. Considering matchgate circuits, generated by time-dependent spin-1/2 XY Hamiltonians, we give an…
The numerical quantum electronic structure for the energies of the states of the hydrogen like atoms as given by Sommerfeld in 1915-16 is studied and is shown to present a scheme that is able to express a unique observer point of view. The…
A field state containing photons propagating in different directions has a non vanishing mass which is a quantum observable. We interpret the shift of this mass under transformations to accelerated frames as defining space-time observables…
According to Belinsky, Khalatnikov and Lifshitz, gravity near a space-like singularity reduces to a set of decoupled one-dimensional mechanical models at each point in space. We point out that these models fall into a class of conformal…
The orientation in space of a Cartesian coordinate system can be indicated by the two vectorial constants of motion of a classical Keplerian orbit: the angular momentum and the Laplace-Runge-Lenz vector. In quantum mechanics, the states of…
In this letter I stress the role of causal reversibility (time-symmetry), together with causality and locality, in the justification of the quantum formalism. Firstly, in the algebraic quantum formalism, I show that the assumption of…