2015/01/25 by О. В. Веко, O. V. Veko, Veko, O. V. +3
Mathematics · Physics and Astronomy · #33E30 #34B30 #Algebraic and Geometric Analysis #FOS: Physical sciences #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #msc:33E30 #msc:34B30 #quant-ph
paper · pdf · doi:10.48550/arxiv.1501.06175
21 pages
arxiv created 2015/01/25 · openalex publication_date 2015/01/25 · arxiv updated 2015/01/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
It is shown that the known method to solve the Dirac equation by means of the squaring method, when relying on the scalar function of the form Φ= e-iεt e^ik1 x e^ik2 y sin (kz + α) leads to a 4-dimensional space of the Dirac solutions. It is shown that so constructed basis is equivalent to the space of the Dirac states relied on the use of quantum numbers k1, k2, ± k and helicity operator; linear transformations relating these two spaces are found. Application of the squaring method substantially depends on the choice of representation for the Dirac matrices, some features of this are considered. Peculiarities of applying the squaring method in Majorana representation are investigated as well. The constructed bases are relevant to describe the Casimir effect for Dirac and Weyl fields in the domain restricted by two planes.