1 ECE Field Equations – Vector Form Material Equations Dielectric Displacement Magnetic Induction

2 Field-Potential Relations I Potentials and Spin Connections A: Vector potential Φ: scalar potential ω e : Vector spin connection of electric potential ω m : Vector spin connection of magnetic potential ω 0 : Scalar spin connection (electric)

3 ECE Field Equations in Terms of Potential I

4 ECE Field Equations in Terms of Potential with cold currents I ρ e0, J e0 : normal charge density and current ρ e1, J e1 : cold charge density and current

5 Antisymmetry Conditions of ECE Field Equations I All these relations appear in addition to the ECE field equations and are contained in them. They replace Lorenz Gauge invariance and can be used to derive special properties.

6 Field-Potential Relations II Potentials and Spin Connections A: Vector potential Φ: scalar potential ω E : Vector spin connection of electric field ω B : Vector spin connection of magnetic field or

7 ECE Field Equations in Terms of Potential II Version 1

8 ECE Field Equations in Terms of Potential II Version 2

9 ECE Field Equations in Terms of Potential with cold currents II, Version 1 ρ e0, J e0 : normal charge density and current ρ e1, J e1 : cold charge density and current

10 Antisymmetry Conditions of ECE Field Equations II