Related papers: The Negative Energy Sea
A quantum Dirac field theory with no divergences of vacuum energy is presented. The vacuum energy divergence is eliminated by removing a extra degree of freedom of the Dirac fields. The conditions for removing the extra degree of freedom,…
Boltzmann's differential equation is replaced by the corresponding reciprocal symmetric finite difference equation. Finite difference translates discreteness of energy. Boltzmann's function, then, splits into two reciprocally related…
Electrons in materials containing heavy elements are fundamentally relativistic and should in principle be described using the Dirac equation. However, the current standard for treatment of electrons in such materials involves density…
The similarity renormalization group is used to transform a general Dirac Hamiltonian into diagonal form. The diagonal Dirac operator consists of the nonrelativistic term, the spin-orbit term, the dynamical term, and the relativistic…
The perturbation of the Dirac sea to first order in the external potential is calculated in an expansion around the light cone. It is shown that the perturbation consists of a causal contribution, which describes the singular behavior of…
The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the…
Special-relativistic dynamically-generated elementary-particle mass is represented by a self-adjoint energy operator acting on a rigged Hilbert space (RHS) of functions over the 6-dimensional Euclidean-group manifold. The energy operator is…
We open out one of incorrect solutions of the Driac equation in the Coulomb field given in a published paper. By introducing a transformation of function, the paper transformed the original radial first-order Dirac-Coulomb equation into two…
Without invalidating quantum mechanics as a principle underlying the dynamics of a fundamental theory, it is possible to ask for even more basic dynamical laws that may yield quantum mechanics as the machinery needed for its statistical…
We represent sixteen-component values "sedeons", generating associative noncommutative space-time algebra. We demonstrate a generalization of relativistic quantum mechanics using sedeonic wave functions and sedeonic space-time operators. It…
The Dirac equation is used to provide a relativistic calculation of the binding energy of a hydrogen-like atom confined within a penetrable spherical barrier. We take the potential to be Coulombic within the barrier and constant outside the…
A model for gravitational collapse where the event horizon is a quantum critical phase transition is extended to provide an explanation for the origin of the observable universe, where the expanding universe that we observe today was…
As the first step in an approach to the solution of Hilbert's sixth problem, a general scheme of mechanics, called `supmech', is developed integrating noncommutative symplectic geometry and noncommutative probability theory in an algebraic…
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…
Dirac's Poisson-bracket-to-commutator analogy for the transition from classical to quantum mechanics assures that for many systems, the classical and quantum systems share the same algebraic structure. The quantum side of the analogy…
In this work we argue against the interpretation that underlies the "Standard" account of Quantum Mechanics (SQM) that was established during the 1930s by Niels Bohr and Paul Dirac. Ever since, following this orthodox narrative, physicists…
The Dirac approach to constrained systems can be adapted to construct relativistic invariant theories on a noncommutative (NC) space. As an example, we propose and discuss relativistic invariant NC particle coupled to electromagnetic field…
Non-radiative solutions of energy critical wave equations are such that their energy in an exterior region $|x|>R+|t|$ vanishes asymptotically in both time directions. This notion, introduced by Duyckaerts, Kenig and Merle (J. Eur. Math.…
We first present a new Lagrangian of general relativity, which can be divided into kinetic energy term and potential energy term. Taking advantage of vierbein formalism, we reduce the kinetic energy term to a sum of five positive terms and…
Quantum theory and Lorentz structure are the twin pillars of fundamental physics today. With quantum theory kept and Lorentz structure replaced by Euclidean Jordan algebra --- a more fundamental structure, one naturally arrives at the…