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Quantum field theory in curved spacetime (QFTCS) is a field of study that focuses on problems that arise when considering a quantum field on a fixed, curved spacetime. It allows the study of quantum effects in strong gravitational fields, and has led to many interesting conclusions, such as the Unruh effect and the Hawking effect.
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Derivation of Dirac equation in curved spacetime
In all the Literature I have read, the covariant Dirac equation in curved spacetime is given as
\begin{equation} \left(i\hbar\gamma^{\mu}(x)\left[\frac{\partial}{{\partial}x^{\mu}}-{\Gamma}_{\mu}(x)\ …