Chanyal, B.C.Sandhya2019-09-162019-09-162019-08http://krishikosh.egranth.ac.in/handle/1/5810128443The Dirac relativistic wave equation combines the special relativity with quantum mechanics that overcomes the difficulties arising in Klein-Gordon equation. In present study, to construct the generalized Dirac equation for rotating particles in four-dimensional Euclidean space-time, we used the quaternionic algebra. Quaternionic algebra is generally an extension of two-dimensional complex numbers. The unitary group SU(2) which is related to the quaternionic rotation group, is isomorphic to the orthogonal group SO(3). The quaternionic moment of inertia and rotational energymomentum quaternion have been discussed by using four-vector representation of relativistic mass, space-time and energy-momentum in quaternionic form. Further, the quaternionic rotational Dirac matrices are introduced with the help of SU(2) group representation, and also derived the quaternionic form of rotational Dirac equation. A novel approach to quaternionic rotational Dirac equation contains rotational energy corresponding to the coefficient of scalar unit element (e0) and the rotational momentum corresponding to the coefficient of vector unit elements (ej). The rotational energy and rotational momentum solutions are obtained by using one, two and four component forms of quaternionic wave function. We have obtained the rotational energy solutions for positive and negative energy of particles with spin up and spin down states. The quaternionic form of positive energy relates with the existence of particle and negative energy relates with the existence of anti-particle. On the other hand, the solutions of quaternionic rotational momentum are obtained which shows the motion of rotating particles and anti-particles in spin up and spin down states. We have also expressed the quaternionic continuity equation for rotational energy and rotational momentum, where these continuity equations represent the conservation of four-current density. To considering the wave nature of Dirac-particles (or anti-particles), we have studied the general form of quaternionic wave function and developed the quaternionic form of rotational frequency and wave vector for particles and anti-particles. Therefore, the present thesis deals with the quaternionic quantum theory for spin-1/2 fermions and anti-fermions with rotating motion.ennullThesis