Editorial Note with a mathematical and historical introduction to a 1932
paper by Erwin Schr\”odinger on the generalization of the Dirac equation to a
curved spacetime — to appear in the ‘Golden Oldie’ section of the Journal of
General Relativity and Gravitation alongside an English translation of that
paper. The Schr\”odinger paper is of interest as the first place that the
well-known formula $g^{\mu\nu}\nabla_\mu\nabla_\nu + m^2 + \frac{R}{4}$ was
obtained for the ‘square’ of the Dirac operator in curved spacetime. This
formula is known by a number of names and we explain why we favour the name
‘Schr\”odinger-Lichnerowicz formula’. We also aim to explain how the modern
notion of `spin connection’ emerged from a debate in the physics journals in
the period 1929-1933. We discuss the key contributions of Weyl, Fock and Cartan
and explain how and why they were partly in conflict with the approaches of
Schr\”odinger and several other authors. We reference and comment on some
previous historical accounts of this topic.
