Related papers: Quantum Trajectories: Dirac, Moyal and Bohm

In this paper we discuss the relevance of the algebraic approach to quantum phenomena first introduced by von Neumann before he confessed to Birkoff that he no longer believed in Hilbert space. This approach is more general and allows us to…

I review the various algebraic foundations of quantum mechanics. They have been suggested since the birth of this theory till up to last year. They are the following ones: Heisenberg-Born-Jordan (1925), Weyl (1928), Dirac (1930), von…

Dirac talked about q-numbers versus c-numbers. Quantum observables are q-number variables that generally do not commute among themselves. He was proposing to have a generalized form of numbers as elements of a noncommutative algebra. That…

The experimental results of Kocsis et al., Mahler et al. and the proposed experiments of Morley et al. show that it is possible to construct "trajectories" in interference regions in a two-slit interferometer. These results call for a…

One key theme of Basil Hiley's work was the development of David Bohm's approach to Quantum Mechanics; in particular the concept of the quantum potential. Another theme was the importance of Clifford Algebras in fundamental physics. In this…

In this paper we show how Dirac, in 1947, anticipated the Bohm approach using an argument based on what is now called the Heisenberg picture. From a detailed examination of these ideas, we show that the role played by the Dirac standard ket…

Quantum algebraic observables representing localization in space-time of a Dirac electron are defined. Inertial motion of the electron is represented in the quantum algebra with electron mass acting as the generator of motion. Since…

We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive…

We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…

A quantum model based on a Euler-Lagrange variational approach is proposed. In analogy with the classical transport, our approach maintain the description of the particle motion in terms of trajectories in a configuration space. Our method…

Geometrical model for quantum objects is suggested. It is shown that equations for free material Dirac field and for Maxwell electromagnetic field can be considered as relations describing propagation of the space topological defects. This…

Credible reasons are presented to reveal that many of the lingering century old enigmas, surrounding the behavior of at least an individual quantum particle, can be comprehended in terms of an objectively real specific wave function. This…

Topological physics has broadened its scope from the study of topological insulating phases to include nodal phases containing band structure singularities. The geometry of the corresponding quantum states is described by the quantum metric…

There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…

A new version of hidden variables theory founded on the generalisation of world's geometry is proposed. The quantum-mechanical motion as the motion in some "inner space", which has a structure of the integrable Weyl space is examined.…

We develop an approach to quantum dynamics based on quantum phase space trajectories. The latter are built from a unitary irreducible representation of the symmetry group of the respective classical phase space. We use a quantum action…

We propose to represent both $n$--qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of dimension $2n.$ In this framework, the Dirac formalism can be realized in…

This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum…

Weak values, obtained from weak measurements, attempt to describe the properties of a quantum system as it evolves from an initial to a final state, without practically altering this evolution. Trajectories can be defined from weak…

To understand the foundations of quantum mechanics, we have to think carefully about how theoretical concepts are rooted in -- and limited by -- the nature of experience, as Bohr attempted to show. Geometrical pictures of physical phenomena…