Gauge transformation and electromagnetism with biquaternionsM. Tanisli
Anadolu University, Science Faculty, Department of Physics - Eskisehir, Turkey
received 24 November 2005; accepted in final form 18 March 2006
published online 8 April 2006
After defining 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 differantial 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.
03.50.De - Classical electromagnetism, Maxwell equations.
02.10.De - Algebraic structures and number theory.
02.30.Xx - Calculus of variations.
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