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In this study, we develop the generalized Dirac like four-momentum equationfor rotating spin-half particles in four-dimensional quaternionic algebra. Thegeneralized quaternionic Dirac equation consists the rotational energy andangular momentum of particle and anti-particle. Accordingly, we also discussthe four vector form of quaternionic relativistic mass, moment of inertia androtational energy-momentum in Euclidean space-time. The quaternionic fourangular momentum (i.e. the rotational analogy of four linear momentum) predictsthe dual energy (rest mass energy and pure rotational energy) and dual momentum(linear like momentum and pure rotational momentum). Further, the solutions ofquaternionic rotational Dirac energy-momentum are obtained by using one, twoand four-component of quaternionic spinor. We also demonstrate the solutions ofquaternionic plane wave equation which gives the rotational frequency and wavepropagation vector of Dirac particles and anti-particles in terms ofquaternionic form.

A comparative study of quaternionic rotational Dirac equation and its interpretation