Related papers: Applying Classical Geometry Intuition to Quantum S…
In these continuation papers (VI and VII) we are interested in approach the problem of spin from a classical point of view. In this first paper we will show that the spin is neither basically relativistic nor quantum but reflects just a…
Within a geometric and algebraic framework, the structures which are related to the spin-statistics connection are discussed. A comparison with the Berry-Robbins approach is made. The underlying geometric structure constitutes an additional…
Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run…
Classical nonlinear theories are highly successful in describing far-from-equilibrium dynamics of magnets, encompassing phenomena such as parametric resonance, ultrafast switching, and even chaos. However, at ultrashort length and time…
In the operational approach to general probabilistic theories one distinguishes two spaces, the state space of the "elementary systems" and the physical space in which "laboratory devices" are embedded. Each of those spaces has its own…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
The notion of a classical particle is inferred from Dirac quantum fields on a curved space-time, by an eikonal approximation and a localization hypothesis for amplitudes. This procedure allows to define a semi-classical version of the…
This paper introduces several ideas of emergent gravity, which come from a system similar to an ensemble of quantum spin-$\tfrac{1}{2}$ particles. To derive a physically relevant theory, the model is constructed by quantizing a scalar field…
Bernstein polynomials and B\'ezier curves play an important role in computer-aided geometric design and numerical analysis, and their study relates to mathematical fields such as abstract algebra, algebraic geometry and probability theory.…
Penrose's Spin Geometry Theorem is extended further, from $SU(2)$ and $E(3)$ (Euclidean) to $E(1,3)$ (Poincar\'e) invariant elementary quantum mechanical systems. The Lorentzian spatial distance between any two non-parallel timelike…
A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational…
In the search of a mathematical basis for quantum mechanics, in order to render it self-consistent and rationally understandable, we find that the best approach is to adopt E. Cartan's way for discovering spinors; that is to start from…
In this work, we extend the so-called typicality approach, originally formulated in statistical mechanics contexts, to $SU(2)$-invariant spin-network states. Our results do not depend on the physical interpretation of the spin network;…
Emerging possibilities for creating and studying novel plasma regimes, e.g. relativistic plasmas and dense systems, in a controlled laboratory environment also requires new modeling tools for such systems. This brings motivation for…
A model quantum system is proposed to describe position states of a massive body in flat space on large scales, excluding all standard quantum and gravitational degrees of freedom. The model is based on standard quantum spin commutators,…
We study dynamical correlations of two coupled large spins depending on the time and on the spin quantum numbers. In the high-temperature approximation, we obtain analytical expressions for the mutual informations, quantum and classical…
There are six different mathematical formulations of the symmetry group in quantum mechanics, among them the set of pure states $\mathbf{P}$ -- i.e., the set of one-dimensional projections on a complex Hilbert space $H$ -- and the…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
General guidelines for constructing a quantum theory of charged-particle beam optics starting ab initio from the basic equations of quantum mechanics, appropriate to the situation under study. In the context of spin-1/2 particles, these…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…