Take the 2-minute tour ×  I have seen the Dirac equation in
curved space-time written as
$$[i\bar{\gamma}^{\mu}\frac{\partial}{\partial
x^{\mu}}-i\bar{\gamma}^{\mu}\Gamma_{\mu}-m]\psi=0 $$  This
$-i\bar{\gamma}^{\mu}\Gamma_{\mu} $ is the spin connection:  a)
Why is it needed?  b) Why is it minus could it be a plus (is it
due to metric signature)?  c) Is the a suitable method to
calculate it for a given metric e.g FRW space-time?
share|improve this question add comment  2 Answers  This is
standard theory. Try    • Birrell, N. D., & Davies, P. C. W.
(1982). Quantum Fields in Curved Space. Cambridge: Cambridge
University Press. Bog standard Curved space QFT text. Don't
remember how much is said specifically about spinors though.
• Brill, D., & Wheeler, J. (1957). Interaction of Neutrinos and
Gravitational Fields. Reviews of Modern Physics, 29(3), 465–479.
doi:10.1103/RevModPhys.29.465 <-- This paper was particularly
clear from memory.    • Yepez, J. (2011). Einstein’s vierbein
field theory of curved space. G