1. The problem statement, all variables and given/known data Find t(τ), x(τ), y(τ), z(τ) for constant electric field E=E(sinθx+cosθz) and B=Bz, and constant magnetic field where E,B, and θ are all constants. I haven't seen this notation before, and I really just want to know what it means specifically. I know and up indice paired with a down indice essentially gives an inner product, but I don't really know what an up indice paired with an up indice gives me. So this is equation 12.32 in Jackson Electrodynamics that I'm trying to understand. 2. Relevant equations m(d2xα/dτ2)=(e/c)(∂αAβ-∂βAα)(dxβ/dτ) 3. The attempt at a solution Also, the 4 vector potential that I've already calculated is: Aα=(-E(xsinθ+zcosθ),-By,0,0) where E, B and θ are all constants. or Aα=(-E(xsinθ+zcosθ),0,Bx,0) I can't decide which one is more convenient. I've attached an image of my best guess for what that equation means.