Related papers: A Transfer Operator Approach to Relativistic Quant…
In this paper we apply the formalism of the analytical signal theory to the Schrodinger wavefunction. Making use exclusively of the wave-particle duality and the principle of relativistic covariance, we actually derive the form of the…
This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
We obtained the Feynman propagators for a noncommutative (NC) quantum mechanics defined in the recently developed Doplicher-Fredenhagen-Roberts-Amorim (DFRA) NC background that can be considered as an alternative framework for the NC…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
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…
The Koopman--von Neumann equation describes the evolution of a complex-valued wavefunction corresponding to the probability distribution given by an associated classical Liouville equation. Typically, it is defined on the whole Euclidean…
We introduce the Wigner functional representing a quantum field in terms of the field amplitudes and their conjugate momenta. The equation of motion for the functional of a scalar field point out the relevance of solutions of the classical…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
The wave function of quantum mechanics is not a boost invariant and gauge invariant quantity. Correspondingly, reference frame dependence and gauge dependence are inherited to most of the elements of the usual formulation of quantum…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
We demonstrate that the recently introduced linear equation, reformulating the first Friedmann equation, is the first-order WKB expansion of a quantum cosmological equation. This result shows a deeper underlying connection between General…
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…
The objective of this series of three papers is to axiomatically derive quantum mechanics from classical mechanics and two other basic axioms. In this first paper, Schreodinger's equation for the density matrix is fist obtained and from it…
This essay intends to present a novel approach to the concept of "transaction" in quantum physics. Breaking with Cramer's original theory, the transaction is not connected to the simultaneously retarded and advanced spacetime propagation of…
Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables,…
A general quantum-mechanical setting is proposed for the field-antifield formalism as a unique hyper-gauge theory in the field-antifield space. We formulate a Schr\"odinger-type equation to describe the quantum evolution in a "current time"…
Classical mechanics, in the Koopman-von Neumann formulation, is described in Hilbert space. It is shown here that classical canonical transformations are generated by Hermitian operators that are in general noncommutative. This naturally…
Consistent quantum formalism based on the localized basis of the Wannirer functions in Heisenberg and Schrodinger pictures to describe propagation of electromagnetic field in a three dimensional media including diffraction is presented. In…
We give a unitary irreducible representation of the proper Poincar\'e group that leads to an operational version of the classical relativistic dynamics of a massive spinless particle. Unlike quantum mechanics, in this operational theory…