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International Journal of Theoretical Physics

Relativistic quantum mechanics of fermions

Egon Marx

Published Oct 1, 1970• 19 citations
Publisher
DOI
10.1007/bf00671869

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Department ofScience Educationand Research Institute forBasicSciences, EwhaWomansUniversity, Seoul 120-750 Korea(Dated: August 15, 2011)We construct a relativistic quantum mechanics for a boson which sustains the positive definiteparticle probability for the relativistic boson. In this theory, we settle down the well-known 85 yearsold unsolved problem on the particle probability of the Klein-Gordon quantum mechanics. Thesolutions for a boson obtained from our theory possess a negative solution as well as a positive one,similar to those of the Dirac quantum mechanics for a fermion. We next study Lorentz transforma-tion, and a vacuum state with all fermion and boson negative energy levels filled and all fermion andboson positive energy levels empty, so that we can have unification of the bosonic sea and the Diracfermionic one. In this unified sea we investigate the bosonic and fermionic antiparticles associatedwith the unified vacuum on an equal footing, and we obtain a charge conjugation operator to studydecay modes of the particles and antiparticles.I. INTRODUTION
We discuss the following system and its attendant properties. Quantum Correction for Thermodynamic Equilibrium, Entropy, Temperature, and Carnot Cycle, Quantum Interference Experiments, Majorana Fermion, Non-Hamiltonian Quantum Mechanics, Topological Entanglement Entropy, Non-Relativistic Quantum Mechanics, Non-Relativistic And Relativistic Hamiltonians, Klein–Gordon And Dirac Equations, Chirality And Helicity And Other Letters And Editorials Of Similar Nature And Interest............ The full paper: http://www.iiste.org/PDFshare/APTA-PAGENO-379267-383489.pdf
We have studied the scattering problem of relativistic fermions from a quaternionic double Dirac delta potential. We have used Dirac equation in the presence of the scalar and vector potentials in the quaternionic formalism of relativistic quantum mechanics to study the problem. The wave functions of different regions have been derived. Then, using the reflection coefficient, transmission coefficient, and the continuity equation, the scattering problem has been investigated in detail. It has been shown that we have faced some fluctuations in the reflection and transmission coefficients.