On the construction of a Dirac spinor that generates a specified tetrad

Journal Article · Sat Nov 01 04:00:00 EST 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.532177· OSTI ID:544819

Nash, P L ^[1]

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1. Division of Earth and Physical Sciences, The University of Texas at San Antonio, San Antonio, Texas 78249-0663 (United States)

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,{bold 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){sub +}{sup {up_arrow}}{r_arrow}{ovr SO(3,1)}. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 544819
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 11 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
DIRAC EQUATION
MINKOWSKI SPACE
PROPAGATOR
SL GROUPS
SPACE-TIME
SPIN
SPINORS
VECTORS