Abstract
In this article, firstly we study about geometrical applications of split quaternions. Then, we obtain Hamitonian mechanical systems with Split quaternions. Quaternionic and Coquaternionic (split analoque of quaternions) extensions of Hamiltonian mechanics are introduced and are shown as offer a unifying framework for quantum mechanics. This study leads to the possibility of employing algebraic techniques of quaternions and coquaternions to absorbing in quantum mechanics. The founded equations are compared with the Hamiltonian energy equations generally are known and the Hamilton energy equations are obtained in Minkowski space.
Highlights
Many of problems in classical mechanics may be solved based on Hamiltonian energy equations using Euclidian space, but none of them are calculated with quaternions
The improvement Hamiltonian energy equations have been proposed on Minkowski space E24 with quaternionic bundle structure
In a different space model, jet bundle structure adapted to quaternions has been constituted
Summary
Many of problems in classical mechanics may be solved based on Hamiltonian energy equations using Euclidian space, but none of them are calculated with quaternions. We prefer to solve Hamiltonian energy equations with quaternions on a jet bundle structure. The metric for quaternions is embedded in Hamiltonian rule for the field This looks like a way to generate scalars from vectors, but it is more than that. For calculating with only information contained in events requires that a scalar and a 3 dimensional vector form for a field. If the magnitude of the 3 dimensional space vector is less than the time scalar, events are separated by a timelike interval. It requires a speed less than the speed of light to connect the events. According to the structure of split quaternion, this time parameter consist of scalar and vector parts as follow;.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
