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 flat 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 members of the particle close-quote s tetrad, as well as two other spacelike members that are rarely discussed. Also, of particular note is the complex null tetrad formalism that provides a map from a two-component SL(2,C) spinor and its complex conjugate to a tetrad. The inverse problem is studied here. Given a tetrad, a complex Dirac spinor valued function of the tetrad is explicitly defined in such a way that certain sums of bilinear products of the components of this spinor exactly reproduce the tetrad. This spinor may be used in the Feynman propagator representation of the solution to the Dirac equation to generate a Dirac wave spinor with desired initial properties. The mappings studied here represent a new class of nonlinear mappings SO(3,1)+↑→SO(3,1). copyright 1997 American Institute of Physics