Related papers: An Algebraic Approach to Koopman Classical Mechani…
In this paper we study the Hilbert space structure underlying the Koopman-von Neumann (KvN) operatorial formulation of classical mechanics. KvN limited themselves to study the Hilbert space of zero-forms that are the square integrable…
In this paper we study the classical Hilbert space introduced by Koopman and von Neumann in their operatorial formulation of classical mechanics. In particular we show that the states of this Hilbert space do not spread, differently than…
We give a formulation of classical mechanics in the language of operators acting on a Hilbert space. The formulation given comes from a unitary irreducible representation of the Galilei group that is compatible with the basic postulates of…
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules…
The classical and quantum features of Nambu mechanics are analyzed and fundamental issues are resolved. The classical theory is reviewed and developed utilizing varied examples. The quantum theory is discussed in a parallel presentation,…
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…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
We demonstrate the existence of a complex Hilbert Space with Hermitian operators for calculations in \textit{classical} electromagnetism that parallels the Hilbert Space of quantum mechanics. The axioms of this classical theory are the…
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…
This work is to consolidate current literature on Koopman-von Neumann (KvN) Mechanics into a simple and easy to understand text. KvN Mechanics is a branch of Classical Mechanics that has been recast into the mathematical language of Quantum…
Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. More precisely, is it possible to capture certain quantum idiosyncrasies within the symplectic…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…
Nelson's stochastic mechanics links quantum mechanics to an underlying Brownian motion with the identification $\hbar = m\sigma$. Ghose's interpolating equation introduces a continuous parameter $\lambda$ that suppresses the quantum…
This thesis is concerned with the representation theory of the Heisenberg group and its applications to both classical and quantum mechanics. We continue the development of $p$-mechanics which is a consistent physical theory capable of…
We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
Based on Koopman formalism for classical statistical mechanics, we propose a formalism to define hybrid quantum-classical dynamical systems by defining (outer) automorphisms of the C*-algebra of hybrid operators and realizing them as linear…