We report the simplest possible form to compute rotations around arbitrary
axis and boosts in arbitrary directions for 4-vectors (space-time points,
energy-momentum) and bi-vectors (electric and magnetic field vectors) by
symplectic similarity transformations. The Lorentz transformations are based
exclusively on real 4×4-matrices and require neither complex numbers
nor special implementations of abstract entities like quaternions or Clifford
numbers. No raising or lowering of indices is necessary. It is explained how
the Lorentz transformations can be derived from the most simple second order
Hamiltonian of general significance. Since this approach exclusively uses the
real Clifford algebra Cl(3,1), all calculations are based on real 4×4
matrix algebra.Comment: Substantial rewrite of first draft. 16 pages, 1 figur