Related papers: Particle Trajectories for Quantum Field Theory
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…
Using Feynman's representation of the quantum evolution and considering a quantum particle as a matter field (continuous medium), it is shown that individual particles of the field have unique paths of the motion. This allows describing…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
Vortices are known to play a key role in the dynamics of the quantum trajectories defined within the framework of the de Broglie-Bohm formalism of quantum mechanics. It has been rigourously proved that the motion of a vortex in the…
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…
In this thesis we study the de Broglie-Bohm pilot-wave interpretation of quantum theory. We consider the domain of non-relativistic quantum theory, relativistic quantum theory and quantum field theory, and in each domain we consider the…
We develop a non-relativistic quantum field theory of electrons and nuclei based on the Coulomb Hamiltonian. We derive the exact equations of motion and write these equations in the form of Hedin's equations for all species of identical…
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
Pilot-wave theories provide possible solutions to the measurement problem. In such theories, quantum systems are not only described by the state vector, but also by some additional variables. These additional variables, also called beables,…
We describe the picture of physical processes suggested by Edward Nelson's stochastic mechanics when generalized to quantum field theory regularized on a lattice, after an introductory review of his theory applied to the hydrogen atom. By…
We give a relativistically covariant, wave-functional formulation of Bohm's quantum field theory for the scalar field based on a general foliation of space-time by space-like hypersurfaces. The wave functional, which guides the evolution of…
Quantum systems in specific regimes display recurrences at the period of the periodic orbits of the corresponding classical system. We investigate the excited hydrogen atom in a magnetic field -- a prototypical system of 'quantum chaos' --…
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…
Complexified Lienard-Wiechert potentials simplify the mathematics of Kerr-Newman particles. Here we constrain them by fiat to move along Bohmian trajectories to see if anything interesting occurs, as their equations of motion are not known.…
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…
Quantum mechanics is the most successful theory to describe microscopic phenomena. It was derived in different ways over the past 100 years by Heisenberg, Schr\"{o}dinger, and Feynman. At the same time, other interpretations have been…
We analyze the dynamics of a quantum particle in a one-dimensional bistable potential within the framework of Bohm's quantum mechanics. We give arguments that evidence the fallacy of certain claims found in the literature dealing with the…
We generalize the de Broglie-Bohm (dBB) formulation of quantum mechanics to the case of quantum gravity (QG) by using the effective action for a QG theory. This is done by replacing the dBB equations of motion with the effective action…
Non-relativistic quantum particles in the Earth's gravitational field are successfully described by the Schr\"{o}dinger equation with Newton's gravitational potential. Particularly, quantum mechanics is in agreement with such experiments as…
In this study, we use the concept of Bohmian trajectories to present a dynamical and deterministic interpretation for the gravity induced wave function reduction. We shall classify all possible regimes for the motion of a particle, based on…