Related papers: A geometrical dual to relativistic Bohmian mechani…
It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally "curved" space-time. This shows that it is possible to formulate quantum…
In this article we show that the fundamental equations of relativistic Bohmian mechanics for a single particle can be derived from a scalar theory of curved space-time.
The causal stochastic interpretation of relativistic quantum mechanics has the problems of superluminal velocities, motion backward in time and the incorrect non-relativistic limit. In this paper, according to the original ideas of de…
Conventional relativistic quantum mechanics, based on the Klein-Gordon equation, does not possess a natural probabilistic interpretation in configuration space. The Bohmian interpretation, in which probabilities play a secondary role,…
Positive-energy solutions of the Klein-Gordon equation form a Hilbert space of holomorphic functions on the future tube. This domain is interpreted as an extended phase space for the associated classical particle, the extra dimensions being…
We construct a relativistic quantum mechanics for a boson. To do this we exploit two component wave functions in Dirac type equations of motion. In our formalism we fix the pathological aspect of particle probability density which appears…
In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum…
Even though the Bohmian trajectories given by integral curves of the conserved Klein-Gordon current may involve motions backwards in time, the natural relativistic probability density of particle positions is well-defined. The Bohmian…
The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided…
I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle…
We show that there exists a duality between the local coordinates and the solutions of the Klein-Gordon equation in curved spacetime in the same sense as in the Minkowski spacetime. However, the duality in curved spacetime does not have the…
In classical relativistic mechanics, a "preferred" proper direction in spacetime for each particle is determined by the direction of its 4-momentum. Analogously, for each quantum particle we find a local direction uniquely determined by the…
Two alternative ways of description an evolution constrained by mass-shell equation are given by the hyperbolic and the periodic angles. In the both cases the angles are proportional to the mass. The differential operators with respect to…
This article develops a variational formulation of relativistic nature applicable to the quantum mechanics context. The main results are obtained through basic concepts on Riemannian geometry. Standards definitions such as vector fields and…
Quantum theory is formulated as a probabilistic theory on a flat Minkowski space-time, while general theory of relativity is formulated on a curved manifold as a geometric theory. Bohmian Quantum Gravity approach indicates that one need to…
A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating…
Bohmian mechanics, also referred to as the de Broglie-Bohm pilot-wave theory, represents a deterministic and nonlocal interpretation of quantum mechanics. Since its origination in 1927, despite many attempts, reconciling it with…
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…
We use the Klein-Gordon equation in a curved spacetime to construct the relativistic analog of the Schr\"odinger-Newton problem, where a scalar particle lives in a gravitational potential well generated by its own probability distribution.…
Bohmian mechanics is an interpretation of quantum mechanics that describes the motion of quantum particles with an ensemble of deterministic trajectories. Several attempts have been made to utilize Bohmian trajectories as a computational…