Foldy-Wouthuysen Transformations Research Articles

Equivalent representations of the Dirac equation

A simple analogy between Foldy-Wouthuysen transformations and two-dimensional rotations is pointed out and from that a new (equivalent) form of the Dirac Hamiltonian is obtained. It is shown that this Hamiltonian is suitable for the discussion of massless fermions, the corresponding wave functions in the new presentation being directly given in terms of two-component spinors.

A new treatment of relativistic terms in the APW-method

A new formulation of relativistic APW is presented, which solves a two-component equation, following from the full relativistic Dirac-equation by two Foldy-Wouthuysen transformations. The two-component Hamiltonian contains the mass-velocity, Darwin and spin-orbit-coupling terms. This APW-method results in a secular equation which is very similar to the nonrelativistic and also to the completely relativistic ones.

Note on relation between Foldy-Wouthuysen and Lorentz transformations

Note on relation between Foldy-Wouthuysen and Lorentz transformations

Relation between Generalized Foldy-Wouthuysen and Lorentz Transformations

A relation between the generalized Foldy-Wouthuysen, presented in a preceding paper, and the special Lorentz transformations is shown.

Operator equations for foldy-wouthuysen transformations

The one-particle Hamiltonians ψ+ and ψ-_, introduced by Snyder and Weinberg for charged scalar fields in a static electromagnetic field, are derived by diagonalizing the matrix Hamiltonian which is at the basis of the Sakata-Taketani formulation of wave mechanics of spin-zero particles. The analogous problem for spin-one particles in a static electromagnetic field is also discussed.

Relation between Foldy-Wouthuysen and lorentz transformations

It is shown that, in the Dirac theory of a free electron, the Foldy-Wouthuysen transformation corresponds to the Lorentz transformation from the laboratory to the rest system of the electron, together with a factor which preserves the norm of the wave function. This consideration resolves the ambiguity in the Foldy-Wouthuysen transformation. Also it is shown that covariantly-defined Lorentz-tensor operators may be interpreted as Lorentz transforms of matrix operators from the rest to the laboratory system.