ON THE CONSTRUCTION OF A DIRAC SPINOR THAT GENERATES A SPECIFIED TETRAD

It is well known that a complex four-component Dirac spinor defines an orthonormal tetrad on hat Minkowski spacetime, For example, a spinor solution to the Dirac equation determines the four-velocity and Pauli- Lubanski spin vector, comprising the timelike and first spacelike memb ers of the particle's tetrad, as well as two other spacelike members t hat are rarely discussed. Also, of particular note is the complex null tetrad formalism that provides a map from a two-component SL (2, C) s pinor and its complex conjugate to a tetrad. The inverse problem is st udied here. Given a tetrad, a complex Dirac spinor valued function of the tetrad is explicitly defined in such a way that certain sums of bi linear products of the components of this spinor exactly reproduce the tetrad. This spinor may be used in the Feynman propagator representat ion of the solution to the Dirac equation to generate a Dirac wave spi nor with desired initial properties. The mappings studied here represe nt a new class of nonlinear mappings SO(3,2)(+)(1) --> SO(3,1). (C) 19 97 American Institute of Physics.