相关论文: Probability and Dirac equation

Drawing from the optimal transport theory adapted to the relativistic setting we formulate the principle of a causal flow of probability and apply it in the wave packet formalism. We demonstrate that whereas the Dirac system is causal, the…

The classical equation of motion of a charged point particle, including its radiation reaction, is described by the Lorentz-Dirac equation. We found a new class of solutions that describe tunneling (in a completely classical context!). For…

Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution…

After the short survey of the Klein Paradox in 3-dimensional relativistic equations, we present a detailed consideration of Dirac modified equation, which follows by one particle infinite overweighting in Salpeter Equation. It is shown,…

The derivation becomes possible when we find a new formalism which connects the relativistic mechanics with the quantum mechanics. In this paper, we explore the quantum wave nature from the Newtonian mechanics by using a concept: velocity…

Spin is a fundamental degree of freedom, whose existence was proven by Dirac for an electron by imposing the relativity to quantum mechanics, leading to the triumph to derive the Dirac equation. Spin of a photon should be linked to…

We derive the neutrino oscillation probabilities including sterile neutrinos by using the Dirac equation. If neutrinos have both the Dirac and the Majorana mass terms, left-handed neutrino $\nu_L$ and right-handed anti-neutrino $\nu_R^c$…

A method of quantizing parametrized systems is developed that is based on a kind of ``gauge invariant'' quantities---the so-called perennials (a perennial must also be an ``integral of motion''). The problem of time in its particular form…

A novel method is developed to derive the original Dirac equation and demonstrate that it is the only Poincare invariant dynamical equation for 4-component spinor wavefunctions. New Poincare invariant generalized Dirac and Klein-Gordon…

We consider the behavior of the particles at ultra relativistic energies, for both the Klein-Gordon and Dirac equations. We observe that the usual description is valid for energies such that we are outside the particle's Compton wavelength.…

We survey the classical results of the Dirichlet Approximation Theorem.

The Dirac equation is solved for two novel terms which describe the interaction energy between the half integral spin of a fermion and the classical, circularly polarized, electromagnetic field. A simple experiment is suggested to test the…

In this work, we find the Poisson superalgebras related to schemes of quantization. Initially, we consider the Dirac superbracket in the context of the quantization of constrained systems. Next, we show the existence of a Poisson…

A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.

We solve the single particle Dirac bound state equation with a particular confining potential and comment its significance from the point of view of the quantum field theory. We show that the solutions describe a complex physical system…

A c-number path integral representation is constructed for the solution of the Dirac equation. The integration is over the real trajectories in the continuous three-space and other two canonical pairs of compact variables controlling the…

The theory of radiation of photons from Dirac particles caused by a projective measurement is developed. The explicit expressions for the inclusive probability to record a chain of events that the Dirac fermion had been measured in a…

We discuss the most general form of Dirac equation in the non$-$Riemannian spacetimes containing curvature, torsion and non$-$metricity. It includes all bases of the Clifford algebra $cl(1,3)$ within the spinor connection. We adopt two…

The usual method of solving the free particle Dirac equation results in the so called continuum energy solutions. Here, we take a different approach and find a set of solutions with quantized energies which are proportional to the total…

The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom. But that is unnecessary because all the practical consequences of such predictions follow from the remaining, non-probabilistic,…