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Initial momenta of de Broglie-Bohm trajectories generally do not obey quantum mechanical momentum distributions. The solution to this problem presented in the following leads to an extended hydrodynamic interpretation of quantum mechanics.…
The non-Abelian topological order for superconductors is characterized by the existence of zero-energy Majorana fermions in edges of systems and in a vortex of a macroscopic condensate, which obey the non-Abelian statistics. This paper is…
We compare and contrast two distinct approaches to understanding the Born rule in de Broglie-Bohm pilot-wave theory, one based on dynamical relaxation over time (advocated by this author and collaborators) and the other based on typicality…
The representation of a quantum system as the spatial configuration of its constituents evolving in time as a trajectory under the action of the wave-function, is the main objective of the Bohm theory. However, its standard formulation is…
In De Broglie-Bohm Pilot-Wave Theory unique equations of motion and scalar fields for a particle can be formulated. This is done by finding a solution for a divergence free probability density current $\vec{J}(r,t)$ and then dividing by the…
We consider $\text{SU}(2)$ quantum chromodynamics in $1+1$ dimensions with a single quark in the spin $J$ representation of the gauge group and study the theory in the large $J$ limit where the gauge coupling $g^2 \to 0$ and $J \to \infty$…
A nonrelativistic equation for the system of two interacting particles within the framework of a model with noncommuting operators of coordinates and momenta of different particles is proposed, and a self-consistent system of equations for…
We present the results of low lying excitation of coupled optical cavity arrays. We derive the Dirac equation for this system and explain the existence of Majorana fermion mode in the system. We present quite a few analytical relations…
We present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative…
In the present letter, the dynamics of a spin one-half particle with non abelian charge, interacting with a non abelian monopole like configuration, is studied. In the non spinning case, these equations correspond to the Wong ones [1], and…
We consider a class of nonlinear Klein-Gordon equations which are Hamiltonian and are perturbations of linear dispersive equations. The unperturbed dynamical system has a bound state, a spatially localized and time periodic solution. We…
In the pilot-wave theory of quantum mechanics particles have definite positions and velocities and the system evolves deterministically. The velocity of a particle is determined by the wave function of the system (the guidance equation) and…
In recent years there has been an intensive search for Majorana fermion states in condensed matter systems. Predicted to be localized on cores of vortices in certain non-conventional superconductors, their presence is known to render the…
We show that Majorana particles belong to the Wigner class of fermions in which the charge conjugation and the parity operators commute, rather than anticommute. Rigorously speaking, Majorana spinors do not satisfy the Dirac equation [a…
Quantum mechanics and relativity in the continuum imply the well known spin-statistics connection. However for particles hopping on a lattice, there is no such constraint. If a lattice model yields a relativistic field theory in a continuum…
Majorana fermions have recently garnered a great attention outside the field of particle physics, in condensed matter physics. In contrast to their particle physics counterparts, Majorana fermions are zero energy, chargeless, spinless,…
Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing to bound the error made by mean-field approaches. Such…
We introduce exactly solvable models of interacting (Majorana) fermions in $d \ge 3$ spatial dimensions that realize a new kind of topological quantum order, building on a model presented in ref. [1]. These models have extensive topological…
In several self-coupled quantum field theories when treated in semi-classical limit one obtains solitonic solutions determined by topology of the boundary conditions. Such solutions, e.g. magnetic monopole in unified theories…
We discuss a class of quantum Abraham models in which the N-particle spinor wave function of N electrons solves a Pauli respectively Schroedinger equation, featuring regularized classical electromagnetic potentials which solve the…