Poincaré invariance

Every isometry of flat 4D spacetime, the ten solutions of Killing’s equation, and what they imply: charges, particles, aberration, precession.

∂_μξ_ν + ∂_νξ_μ = 0⟹ξ^μ = a^μ + ω^μ_ν x^ν 4 translations + 3 rotations + 3 boosts = 10, with ω_μν = −ω_νμ, η = diag(+1,−1,−1,−1)