Resumo

FORMIGA, J.B.. The Frenet-Serret description of Born rigidity and its application to the Dirac equation. Rev. mex. fis. [online]. 2020, vol.66, n.2, pp.180-186.  Epub 26-Mar-2021. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.66.180.

The role played by non-inertial frames in physics is one of the most interesting subjects that we can study when dealing with a physical theory. This is especially true for special relativity and the Dirac theory In the case of special relativity, a problem with the concept of rigidity emerged as soon as Max Born gave a reasonable definition of rigid motion: the Herglotz-Noether theorem imposes a strong restriction on the possible rigid motions. In this paper, the equivalence of this theorem with another one that is formulated with the help of Frenet-Serret formalism is proved, showing the connection between the rigid motion and the curvatures of the observer’s trajectory in spacetime. Besides, the Dirac equation in the Frenet-Serret frame for an arbitrary observer is obtained and applied to the rotating observers. The solution in the rotating frame is given in terms of that of an inertial one.

Palavras-chave : Born rigidity; accelerated frames; Dirac equation; rotating observers; Frenet-Serret formalism; 03.30.+p; 03.65.-w; 02.40.-k.

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