The intermediate fermionic species created by $SO(3)$ rotation in the representation of the Dirac equation

H. Moaiery; M. N. Najafi

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arXiv · 2010.02698

The intermediate fermionic species created by $SO(3)$ rotation in the representation of the Dirac equation

H. Moaiery·M. N. Najafi

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Abstract

The question of how does the Dirac equation depend on the choice of the $\gamma$ matrices has partially been addressed and explored in the literature. In this paper we focus on this question by considering a general form of $\gamma$ matrices, and call the resulting spin $\frac{1}{2}$ fermions as \textit{intermediate fermion species} (IFS). By inspecting the properties of IFS, we find that all species transform to each other by a $SO(3)$ similarity transformation in the space of parameters, that are the entities of the $\gamma$ matrices. Many properties, like eigenvalue problem and boost are tested for IFS. We find also sub-representations that generate Majorana fermions, which is isomorphism to $U(1)$ group.

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H. Moaiery, M. N. Najafi. 2020-09-22. The intermediate fermionic species created by $SO(3)$ rotation in the representation of the Dirac equation. https://arxiv.org/abs/2010.02698

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