- #1

the_viewer

- 3

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It's possible to construct a electromagnetic field, such that

[tex]\vec{F}:=\vec{E} + i\cdot \vec{B}[/tex].

Now the real part is the electric and the imaginary part is the magnetic field.

Then, for example, the maxwell equations take the form

[tex]\nabla \cdot \vec{F} = \rho, \qquad \rho \in \mathbb{R} [/tex]

and

[tex]\nabla\times \vec{F} - i \cdot \frac{\partial}{\partial t} \vec{F} = \vec{j}, \qquad \vec{j} \in \mathbb{R}^3 [/tex]

So, it is possible to combine electric and magnetic field into

*one*(complex) Field.

Now my question: Is something similar possible for the electromagnetic potentials [tex]\Phi[/tex] and [tex]\vec{A}[/tex]?

My idea is to combine the scalar and vector potential into

*one*quaternionic potential.

(Each quaternion consists of an scalar part and an vector part, so somehow it seems possible...)

If possible: How do the field equations look like with such an potential?

Or is there a different possibility to "unify" these two potentials?

Thanks,

David