On the Synergic Relationships between Special Relativity and Quantum Theories

The successful results of the relativistic form of a quantum field theory that is derived from aLagrangian density justify its general usage. The significance of the Euler-Lagrange equations of a quantum particle is analysed. Many advantages of this approach, like abiding by the conservation laws of energy, momentum, angular momentum, and charge are well known. The merits of this approach also include other properties that are still not well known. For example, it is shown that a quantum function of the form ψ(t, r) describes a pointlike particle. Furthermore, the Lagrangian density and the Hamiltonian density take a different relativistic form – the Lagrangian density is a Lorentz scalar, whereas the Hamiltonian density is the T00 component of the energy-momentum tensor. It is proved that inconsistencies in the electroweak theory stem from negligence of the latter point.

Preliminary Empirical study of the Rayleigh to Compton scattering ratio for elements at gamma energy 59.5 keV using Si(Li) detector

The characteristic parameters of a material relation to photon interactions such as: mass attenuation coefficient, effective atomic number, effective electron density are required to provide essential data in diverse works such as nuclear diagnostic and cancer radiotherapy, industrial irradiation, radiation dosimetry, radiation protection and shielding, analyzing of the concentration of elements and radioactive isotopes. In this paper, the theoretical models such as non-relativistic form factor (NRFF), relativistic form factor (RFF), and modified form factor (MFF) were used to calculate the ratio Rayleigh-Compton for elements with at gamma energy 59.5 keV. The results showed that there was a discrepancy between the theoretical modes at a high atomic number. The mean value of the Rayleigh-Compton ratio depends on the atomic number, which shows the quadratic function of the correlation coefficient R2 = 0.996 as well. Besides, the experimental system was set-up and measured for some targets such as aluminum, copper, and lead at a scattering angle 150o using 241Am source by Si(Li) detector to confirm the theoretical values. The preliminary result showed that there was a good agreement with experimental and theoretical results is lower than 20%. Further investigation will be measured by the samples for more detailed evaluation.

Dirac’s Derivation of the Relativistic Wave Equation

The problem of electron spin was in some way connected with special relativity. Dirac’s fascination with relativity and his already burgeoning reputation made the search for a fully relativistic form of the new quantum mechanics irresistible. An important clue was available in a treatment that Pauli had published in 1927, in which he had represented the spin angular momemtum operators as 2 × 2 Pauli spin matrices. Dirac presumed that a proper relativistic wave equation could be derived simply by extending the spin matrices to a fourth member, but quickly realized this couldn’t be the answer. As he played around with the equations, in 1928 he found that he needed 4 × 4 matrices, instead. This allowed him to derive a relativistic wave equation, and to show that electron spin was indeed the result. The two extra solutions were subsequently shown to belong to the positron. Dirac had discovered antimatter.

Calculation of Acceleration Effects Using the Zubarev Density Operator

The relativistic form of the Zubarev density operator can be used to study quantum effects associated with acceleration of the medium. In particular, it was recently shown that the calculation of perturbative corrections in acceleration based on the Zubarev density operator makes it possible to show the existence of the Unruh effect. In this paper, we present the details of the calculation of quantum correlators arising in the fourth order of the perturbation theory needed to demonstrate the Unruh effect. Expressions for the quantum corrections for massive fermions are also obtained.

Quantum-Relativistic Effects at the Nanolevel: Analysis of the Mean Square Deviation of Position with a new Analytical Model

In this paper I present new results about the quantum-relativistic form of the mean squaredeviation of position related to a recently appeared Drude-Lorentz-like model alreadyperformed in classical and quantum way, named DS model. The model gives preciseinformations about the distance traveled by a carrier (electrons, ions, etc.) inside ananostructure in the hypothesis of quantum effects and relativistic velocity. It has a widescale range of applicability; I consider the nanoscale in this paper, but the model holdsfrom sub-pico-level to macro-level because of the presence of a gauge factor, making itapplicable to all oscillating processes in Nature. Examples of application and suggestions complete the paper.