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| The current formalisms of covariant derivatives for a spinor take compact forms, and the geometrical and dynamical effects of the spinor connection are covered under the abstract symbols. The practical calculations for the spinor connection in these formalisms are usually a tiresome and fallible task. In this paper, we divide the spinor connection into two vectors $\\Upsilon_\\mu$ and $\\Omega_\\mu$, where $\\Upsilon_\\mu$ is mainly related to the geometrical calculations, but $\\Omega_\\mu$ leads to gravimagnetic effects. The expression is valid for both the Weyl spinor and the Dirac bispinor, which is not only more convenient
for calculation, but also highlights the physical meanings of the spinor connection. On this foundation, we derive the complete classical mechanics from the dynamical equation and get some interesting results. We find in the space-time with intrinsically nondiagonal metric, the orbit of a spinor deviates from the geodesic slightly, so the principle of equivalence is broken by the spinors moving at high speed. |
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| Keywords:spinor connection;covariant derivative;gravimagnetic field;principle of equivalence |
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