Related papers: Emergent Classicality via Commuting Position and M…
In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz-Pauli constraints via three different methods: the eigenvalue equations for the Casimir…
We investigate operator algebraic origins of the classical Koopman-von Neumann wave function $\psi_{KvN}$ as well as the quantum mechanical one $\psi_{QM}$. We introduce a formalism of Operator Mechanics (OM) based on a noncommutative…
The quantum measurement problem, the unresolved conflict between the unitary evolution of the wave function and the postulate of wave function collapse, remains the most profound conceptual challenge in quantum foundations. While…
Sequences of actions do not commute.. For example, the tick of a clock and the measurement of a position do not commute with one another, since the position will have moved to the next position after the tick. We adopt non-commutative…
This is a pedagogical paper where we present a physically motivated approach to introduce the coherent states of a harmonic oscillator from which it is simple to rigorously derive their mathematical definition. We do this in two different…
Classical and quantum physics represent two distinct theories; however, quantum physics is regarded as the more fundamental of the two. It is posited that classical mechanics should arise from quantum mechanics under certain limiting…
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative point of view in which…
Classical mechanics is presented here in a unary operator form, constructed using the binary multiplication and Poisson bracket operations that are given in a phase space formalism, then a Gibbs equilibrium state over this unary operator…
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…
In the past ten-fifteen years, stochastic models of continuous wave function collapse were being proposed to describe the continuous emergence of classicality from quantum. We advocate that the hybrid dynamics of canonically coupled quantum…
We consider the quantum-to-classical transition for macroscopic systems coupled to their environments. By applying Born's Rule, we are led to a particular set of quantum trajectories, or an unravelling, that describes the state of the…
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…
Following the same steps made for a scalar field in a parallel publication, we propose a class of perturbative theories of quantum gravity based on fractional operators, where the kinetic operator of the graviton is either made of…
We investigate the classical aspects of Quantum theory and under which description Quantum theory does appear Classical. Although such descriptions or variables are known as "ontological" or "hidden", they are not hidden at all, but are…
The model of the position-dependent noncommutativety in quantum mechanics is proposed. We start with a given commutation relations between the operators of coordinates [x^{i},x^{j}]=\omega^{ij}(x), and construct the complete algebra of…
A recent formalism capturing the classical-quantum coupling in a Hamiltonian theory for probabilistic classical mechanics has been proposed: the Koopman-van Hove formulation. The aims of this report are twofolds. First, we rigourously…
The understanding of how classical dynamics can emerge in closed quantum systems is a problem of fundamental importance. Remarkably, while classical behavior usually arises from coupling to thermal fluctuations or random spectral noise, it…
Quantum mechanics is nonlocal. Classical mechanics is local. Consequently classical mechanics can not explain all quantum phenomena. Conversely, it is cumbersome to use quantum mechanics to describe classical phenomena. Not only are the…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…