Gauge transformation and electromagnetism with biquaternions

Abstract

After de. ning biquaternions with complex numbers, the algebra of biquaternions and some properties are introduced. Maxwell's equations without sources in the dimensionless form are given. Then Maxwell's equations are derived in terms of the biquaternionic representations of differential vector operator, electromagnetic bivector. A first-order Lagrangian description is given using the biquaternionic representation of Maxwell's equations. Local energy conservation equation for electromagnetic field is obtained from the biquaternionic form of gauge transformation of the electromagnetic bivector. The purpose is to provide an alternative with biquaternions for the usual derivations which are based on time translation. At the end, the density and flow of electromagnetic energy are attained.