2. Symbols and Conventions
The following standard symbols are used: L and L-1 for the matrices corresponding to the direct and the reciprocal Lorentz transformation, F for the matrix expressing the electromagnetic field, Ji for the charge/current-density four-vector and Ji for his
dual four-form, Vi for the four-velocity and, finally, G for the Gauss matrix characterizing the metric:
In addition, we introduce another matrix M representing the electro-magnetic field and a Nabla-operator as a four-form:
M (more precisely G·M) can be found in literature under the name 'dual fieldtensor' and is denoted with F* oder *F.
The Nabla-operator corresponds to the ∂µ of tensor calculus.
The matrices L , L-1 and G do not change, if they are transposed, and for G holds G-1 = G .
Further we have L-1 = G·L·G and L-1 = G-1·L·G as well as L = G·L-1·G und L = G-1·L-1·G .