Separated Two-Component Equations for Spin-½ Particles Using Foldy-Wouthuysen-Type Transformations with an Application to the k. p. Method in Solids
S. Teitler · Physical Review · 1968
The Foldy-Wouthuysen formalism is presented in a representation-independent manner. It is shown that an algebraic transformation serves to remove the mass term from the Dirac equation for spin-\textonehalf{} particles, thereby providing decoupled two-component equations in a particular (Weyl) representation. Also it is shown that appropriate use of a constant algebraic transformation applied to a Dirac Hamiltonian in the usual (Pauli) representation leads to a nonrelativistic k. p equation used in solid-state theory for which the k-dependent spin-orbit term is absent.