Generalized Foldy-Wouthuysen transformation and pseudodifferential operators. (English. Russian original) Zbl 1274.81069

Theor. Math. Phys. 167, No. 2, 547-566 (2011); translation from Teor. Mat. Fiz. 167, No. 2, 171-192 (2011).
Summary: We show that the Foldy-Wouthuysen transformation and its generalizations are simplified if the methods of pseudodifferential operators are used, which also allow estimating the exactness of the transition from the Dirac equation to the reduced equations for electrons and positrons. The methods and techniques used can be useful not only in studying asymptotic solutions of the Dirac equation but also in other problems.


81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35S05 Pseudodifferential operators as generalizations of partial differential operators
35J10 Schrödinger operator, Schrödinger equation
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