Geometry of the Dirac Theory
نویسنده
چکیده
The Dirac wave function is represented in a form where all its components have obvious geometrical and physical interpretations. Six components compose a Lorentz transformation determining the electron velocity are spin directions. This provides the basis for a rigorous connection between relativistic rigid body dynamics and the time evolution of the wave function. The scattering matrix is given a new form as a spinor-valued operator rather than a complex function. The approach reveals a geometric structure of the scattering matrix and simplifies scattering calculations. This claim is supported by an explicit calculation of the differential crosssection and polarization change in Coulomb scattering. Implications for the structure and interpretation of relativistic quantum theory are discussed.
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