2013/03/22 by Alexander J. Silenko, A. Ya. Silenko
Mathematics · Physics and Astronomy · #Expression (computer science) #Hamiltonian (control theory) #Mathematical functions and polynomials #Operator (biology) #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Representation (politics) #Transformation (genetics) #acm:81-XX #math-ph #math.MP #msc:81-XX
paper · pdf · doi:10.1134/s154747711303014x
published as Physics of Particles and Nuclei Letters 10 (2013) 198 · 7 pages
arxiv created 2013/03/22 · arxiv updated 2013/03/25 · openalex publication_date 2013/05/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The Eriksen method is proven to yield a correct and exact result when a sufficient condition of exact transformation to the Foldy-Wouthuysen (FW) representation is satisfied. Therefore, the Eriksen method is confirmed as valid. This makes it possible to establish the limits within which the approximate “step-by-step” methods are applicable. The latter is done by comparing the relativistic formulas for a Hamiltonian operator in FW representation (obtained using those methods) and the known expression for the first terms of a series, which defines the expansion of this operator in powers of v / c as found by applying the Eriksen method.