I have to compute the square of the Dirac operator, D=γaeμaDμ , in curved space time (DμΨ=∂μΨ+AabμΣab is the covariant derivative of the spinor field and Σab the Lorentz generators involving gamma matrices). Dirac equation for the massless fermion is γaeμaDμΨ=0. In particular I have to show that Dirac spinors obey the following equation: (−DμDμ+14R)Ψ=0 (1) where R is (I guess) the Ricci scalar. Appling to the Dirac eq, the operator γνDν and decomposing the product γμγν in symmetric and antisymmetric part I found: DμDμΨ+14[γμ,γν][Dμ,Dν]Ψ=0 Now I have troubles to show that this last object is related with the Ricci scalar. Can somebody help me or suggest me the right way to solve Eq. (1)?