Abstract
This paper is an extension of [11], where we study the Dirac and spin-Dirac operators associated to different connections. In the present work we present some relations between the Dirac operators associated to the connections on Riemann-Cartan-Weyl spacetime, Riemann-Cartan spacetime and Riemann spacetime. We obtain a generalized Lichnerowicz formula, decompositions of the Dirac and spin-Dirac operators and their squares in terms of the standard Dirac and spin-Dirac operators and using the fact that spinor fields have representatives in the Clifford bundle we present also a noticeable relation involving the spin-Dirac and the Dirac operators.
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