Spinor calculus

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TL;DR
Conventions in spinor calculus
What are the conventions for the spinor metrics and their inverses?
 
Perhaps you could check the Wess–Bagger convention in particle physics.
  • Wess, J., & Bagger, J. (1992). Supersymmetry and Supergravity. Princeton University Press.
  • Two-component spinor techniques by H.K. Dreiner, H.E. Haber, and S.P. Martin (often used to explain these conventions in detail).