  This paper is intended to be a further step through our Killing spinor
programme started with Class. Quantum Grav. \textbf{32}, 175007 (2015), and we
will advance our programme in accordance with the road map recently given in
arXiv:1611.04424v2. In the latter reference many open problems were declared,
one of which contained the uncovered relations between specific spinors in
spacetime represented by an arrow diagram built upon them. This work deals with
one of the arrows with almost all of its details and ends up with an important
physical interpretation of this setup in terms of the quantum electrodynamical
pair annihilation process. This method will shed light on the classification of
pseudo-Riemannian manifolds admitting twistors in connection with the
classification problem related to Killing spinors. Many physical
interpretations are given during the text some of which include dynamics of
brane immersions, quantum field theoretical considerations and black hole
evaporation.
