Related papers: A Krein Quantization Approach to Klein Paradox
This paper deals with the problem of density estimation. We aim at building an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Cand\`es and Tao's approach, we propose an $\ell_1$-minimization…
In this note, we revisit a classical problem related to the density of nonlinear statistics. We obtain a new representation of densities and, for the first time, a necessary and sufficient condition for the existence of densities is…
The Klein Gordon equation was the first attempt at unifying special relativity and quantum mechanics. While initially discarded this equation of "many fathers" can be used in understanding spinless particles that consequently led to the…
The nonlinear quantization of the domain wall (relativistic membrane of codimension 1) is considered. The membrane dust equation is considered as an analogue of the Hamilton-Jacobi equation, which allows us to construct its quantum…
We examine the negative energy solution in Klein-Gordon equation in terms of the number of field components. A scalar field has only one component, and there is no freedom left for an anti-particle since the Klein-Gordon equation failed to…
In the present Chapter, we consider two prototypical Klein-Gordon models: the integrable sine-Gordon equation and the non-integrable $\phi^4$ model. We focus, in particular, on two of their prototypical solutions, namely the kink-like…
A relativistic quantum field theory is presented for finite density problems based on the principle of locality. It is found that, in addition to the conventional ones, a local approach to the relativistic quantum field theories at both…
In this paper we study a gradient flow approach to the problem of quantization of measures in one dimension. By embedding our problem in $L^2$, we find a continuous version of it that corresponds to the limit as the number of particles…
As currently understood since its discovery, the bare Klein-Gordon theory consists of negative quantum probabilities which are considered to be physically meaningless if not outright obsolete. Despite this annoying setback, these negative…
In this paper, we have studied the Klein's paradox in the presence of both scalar and vector potential barriers. From the corresponding Dirac equation we have calculated the transmission and reflection coefficients. It is shown that the…
The Klein Paradox -- the anomalous scattering of relativistic fermions off a high potential step -- signals the limit of the single-particle interpretation of the Dirac equation. While Quantum Field Theory (QFT) resolves this via pair…
Usually the only difference between relativistic quantization and standard one is that the Lagrangian of the system under consideration should be Lorentz invariant. The standard approaches are logically incomplete and produce solutions with…
The Classical Twin Paradox is widely dealt in literature and neatly resolved. In addition, it is also well known that, when looking at two systems which are boosted relative to each other, the concept of the simultaneous effect of a quantum…
The logical inference approach to quantum theory, proposed earlier [Ann. Phys. 347 (2014) 45-73], is considered in a relativistic setting. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from…
We investigate superfluidity, and the mechanism for creation of quantized vortices, in the relativistic regime. The general framework is a nonlinear Klein-Gordon equation in curved spacetime for a complex scalar field, whose phase dynamics…
For free Klein-Gordon fields, we construct a one-parameter family of conserved current densities $J_a^\mu$, with $a\in(-1,1)$, and use the latter to yield a manifestly covariant expression for the most general positive-definite and…
Klein tunneling is a counterintuitive quantum-mechanical phenomenon, predicting perfect transmission of relativistic particles through higher energy barriers. This phenomenon was shown to be supported at normal incidence in graphene due to…
A reference potential approach to the one-dimensional quantum-mechanical inverse problem is developed. All spectral characteristics of the system, including its discrete energy spectrum, the full energy dependence of the phase shift, and…
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,…
Systems with constraints pose problems when they are quantized. Moreover, the Dirac procedure of quantization prior to reduction is preferred. The projection operator method of quantization, which can be most conveniently described by…