Four vector

Four-vectors in a real-valued basis

The upper indices indicate contravariant components. Here the standard convention is that Latin indices take values for spatial components, so that i = 1, 2, 3, and Greek indices take values for time and space components, so α = 0, 1, 2, 3, used with the summation convention. The split between the time component and the spatial components is a useful one to make when determining contractions of one four vector with other tensor quantities, such as for calculating Lorentz invariants in scalar products (examples are given below), or raising and lowering indices.