Аннотация
From the Killing spinor equation and the equations satisfied by their
bilinears we deduce some well known bosonic and fermionic field equations of
mathematical physics. Aside from the trivially satisfied Dirac equation, these
relativistic wave equations in curved spacetimes respectively are Klein-Gordon,
Maxwell, Proca, Duffin-Kemmer-Petiau, Kähler, twistor and Rarita-Schwinger
equations. This result shows that, besides being special kinds of Dirac
fermions, Killing fermions can be regarded as physically fundamental. For the
Maxwell case the problem of motion is analysed in a reverse manner with respect
to the works of Einstein-Groemer-Infeld-Hoffmann and Jean Marie Souriau. In the
analysis of the gravitino field a generalised $3-\psi$ rule is found which is
termed the vanishing trace constraint.
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