Related papers: Quantum Trajectories: Dirac, Moyal and Bohm
Dirac's contributions to the discovery of non-relativistic quantum mechanics and quantum electrodynamics, prior to his discovery of the relativistic wave equation, are described.
Quantum cosmology based on the Wheeler De Witt equation represents a simple way to implement plausible quantum effects in a gravitational setup. In its minisuperspace version wherein one restricts attention to FLRW metrics with a single…
Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here we address a key question which arises in this context: Are…
We show that the Dirac equation can be rewritten as a relation describing the fundamental symmetry group of special topological manifold corresponding to the Dirac wave field. It leads to unification of the time-space and internal…
In this paper we present for the first time a complete description of the Bohm model of the Dirac particle. This result demonstrates again that the common perception that it is not possible to construct a fully relativistic version of the…
Quantum trajectories defined in the de Broglie--Bohm theory provide a causal way to interpret physical phenomena. In this Letter, we use this formalism to analyze the short time dynamics induced by unstable periodic orbits in a classically…
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…
This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be be addressed as well in view of their role in quantum electrodynamics and…
The quantum theory of relativistic particles, based on the first quantization technique similar to that used by Schroedinger and Dirac in formulating quantum mechanics, is reconsidered on the basis of a photon-like dispersion relation…
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
We introduce a pedagogical discussion on Bohmian mechanics and its physical implications in connection with the important role played by the quantum phase in the dynamics of quantum processes. In particular, we focus on phenomena such as…
We illustrate how non-relativistic quantum mechanics may be recovered from a dynamical Weyl geometry on configuration space and an `ensemble' of trajectories (or `worlds'). The theory, which is free of a physical wavefunction, is presented…
We combine the "evolving constants" approach to the construction of observables in canonical quantum gravity with the Page--Wootters formulation of quantum mechanics with a relational time for generally covariant systems. This overcomes the…
A complete theoretical treatment in many problems relevant to physics, chemistry, and biology requires considering the action of the environment over the system of interest. Usually the environment involves a relatively large number of…
One can construct the model conception of quantum phenomena (MCQP) which relates to the axiomatic conception of quantum phenomena (ACQP), (i.e. to the conventional quantum mechanics) in the same way, as the statistical physics relates to…
This colloquium summarizes Dirac's contributions to the discovery of quantum mechanics before he invented his relativistic wave equation.
In describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such differential equations to admit a Lagrangian and/or an Hamiltonian…
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schr\"odinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally,…
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives…