Answer by Qmechanic for A question about covariant derivative on spinor field...
The spinor Laplacian is (1). The square (2) of the Dirac operator minus the spinor Laplacian (1) is a quarter of the scalar Levi–Civita curvature, cf. Weitzenböck-Lichnerowicz identity.
View ArticleA question about covariant derivative on spinor field (Vierbein formalism)
Let's use Latin letters $a,b,c,\cdots$ for local Minkowski frame indices, and Greek letters $\mu,\nu\,\lambda,\cdots$ for coordinate indices.On one hand, we all know that the covariant derivatives for...
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