Electromagnetic Energy Conservation with Octon

Presenter: Murat Tanisli, Anadolu University, Turkey

Joint work with Tulay Tolan, Suleyman Demir

The electromagnetic energy conservation with magnetic monopole in terms of a new algebraic structure named as octon is written. It is known that octons generated from the Clifford algebras by Mironov and Mironov, are a new algebraic structure consisting of four parts as scalar, pseudoscalar, vector and pseudovector and its algebra is associative non-commutative just like quaternions and Pauli algebra. Pauli algebra is the Clifford algebra built on the three basis vectors, which represented by complex quaternions of three-dimensional Euclidean space. Octon algebra can be considered as the variant of complexified Clifford algebra. However, its unit vectors a1, a2, a3 and e1, e2, e3 are real true vectors but not complex numbers. In literature, the octon’s geometrical representations have a clear well-defined geometric interpretation. Here we emphasize once again that octons consist of real scalar and vectors but not hypercomplex numbers, and they are very convenient for physical calculations and symmetry analysis. The imaginary unit in multiplication rules is due to the possibility of Clifford product. Vector (Heaviside-Gibbs) algebra is different from Clifford algebra. Octons have very clear scalar-vector interpretation. The main advantage of octons is pseudoscalar unit a0, which allows one to take into account the symmetry of different physical vectors in accordance with spatial inversion. This is very important from the point of physical applications.