Related papers: Functional methods underlying classical mechanics,…
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
A new formulation of quantum mechanics is proposed based on a new principle that can be considered a generalization of the Born rule. The principle is composed of a mathematical expression and an associated interpretation, and establishes a…
Mechanics can be founded on a principle relating the uncertainty delta-q in the trajectory of an observable particle to its motion relative to the observer. From this principle, p.delta-q=const., p being the q-conjugated momentum,…
Classical Koopman--von Neumann Hilbert spaces of states are constructed here by the action of classical random fields on a vacuum state in ways that support an action of the quantized electromagnetic field and of the $U(1)$--invariant…
We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism,…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
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…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
We develop the general theory of spinning particles with electric and magnetic dipole moments moving in arbitrary electromagnetic, inertial and gravitational fields. Both the quantum-mechanical and classical dynamics is investigated. We…
I assume a universe whereby the speed of light and the planck constant are not constants but instead parameters that vary locally in time-and space. When describing motion, I am able to derive a modified path integral description at the…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman-von Neumann-Sudarshan prescription for classical mechanics on Hilbert spaces {\em sans} the…
The Dirac delta function potential is considered within the real Hilbert space approach for complex wave functions, as well as quaternionic wave functions. As has been previously determined, the real Hilbert space approach enables the…
Considerable effort has been devoted to deriving the Born rule (e.g. that $|\psi(x)|^2 dx$ is the probability of finding a system, described by $\psi$, between $x$ and $x + dx$) in quantum mechanics. Here we show that the Born rule is not…