Related papers: Bohmian Trajectories For a Time Foliation with Kin…
Bohmian mechanics offers a deterministic alternative to conventional quantum theory through well-defined particle trajectories. While successful in nonrelativistic contexts, its extension to curved spacetime-and hence quantum…
First, we survey some results on classical and quantum dynamical systems associated with transverse Dirac operators on Riemannian foliations. Then we illustrate these results by two examples of Riemannian foliations: a foliation given by…
What is the shape of space in a spacetime? One way of addressing this issue is to consider edgeless spacelike submanifolds of the spacetime. An alternative is to foliate the spacetime by timelike curves and consider the quotient obtained by…
We consider the problem of whether there are deterministic theories describing the evolution of an individual physical system in terms of the definite trajectories of its constituent particles and which stay in the same relation to Quantum…
Do the spacetime manifolds which feature in our best scientific theories reflect anything metaphysically weighty in the world (e.g., any fundamental substances or relations)? Should we extend our notions of space and time beyond the…
This paper develops a geometrodynamic extension of Bohmian mechanics to describe quantum tunneling through a potential barrier, treating particle trajectories as geodesics in an Alcubierre-type spacetime. The model provides analytical…
Invariant manifolds are of fundamental importance to the qualitative understanding of dynamical systems. In this work, we explore and extend MacKay's converse KAM condition to obtain a sufficient condition for the nonexistence of invariant…
In this study, we investigate the existence theorems for timelike ruled surfaces in Minkowski 3-space. We obtain a general system and give the existence theorems for a timelike ruled surface according to Gaussian curvature, distribution…
We propose a scenario where the effects of dislocations, in bidimensional Dirac materials at low energies, can be described within a Dirac field theory by a vertex proportional to the totally antisymmetric component of the torsion generated…
It is known that spherically symmetric static spacetimes admit a foliation by {\deg}at hypersurfaces. Such foliations have explicitly been constructed for some spacetimes, using different approaches, but none of them have proved or even…
The paper is a continuation of the works [17] of Vu and Shum, [18] and [19] of Vu and Hoa. In [17], Vu and Shum classified all the MD5-algebras having commutative derived ideals. In [18], Vu and Hoa considered foliations formed by the…
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…
The quantum mechanical motion of a relativistic particle in a non-continuous spacetime is investigated. The spacetime model is a dense, rationale subset of two-dimensional Minkowski spacetime. Solutions of the Dirac equation are calculated…
Bohmian trajectories are considered for a particle that is free (i.e. the potential energy is zero), except for a half-line barrier. On the barrier, both Dirichlet and Neumann boundary conditions are considered. The half-line barrier yields…
The problem of finding null geodesics in a stationary Lorentzian spacetime is known to to be equivalent to finding the geodsics of a Randers-Finlser structure. This latter problem is equivalent to finding the motion of charged particles…
The construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of globally hyperbolic spacetimes. First, we show that any four-dimensional spacetime which admits two commuting and…
We extend the recently proposed Time-Dependent Multi-Determinant approach (ref.[1]) to the description of fermionic propagators. The method hinges on equations of motions obtained using variational principles of Dirac type. In particular we…
The hyperplane and proper time formalisms are discussed mainly for the spin-half particles in the quantum case. A connection between these covariant Hamiltonian formalisms is established. It is showed that choosing the space-like…
The paper is a continuation of the authors' work in which we considered foliations formed by the maximal dimensional K-orbits ($MD_5$-foliations) of connected $MD_5$-groups such that their Lie algebras have 4-dimensional commutative derived…
We construct 2-surfaces of prescribed mean curvature in 3-manifolds carrying asymptotically flat initial data for an isolated gravitating sysqtem with rather general decay conditions. The surfaces in question form a regular foliation of the…