scalar product

The squared norm of a four-vector a = (a_0, a_1, a_2, a_3) = a_0 + a is given by the dot product a^2 congruent a_μ a^μ congruent (a^0)^2 - a·a, where a·a is the usual vector dot product in Euclidean space. Here, the notation a^2 is merely a shorthand for the more descriptive expression a^2 = 〈a, a〉 where 〈·, ·〉 denotes the Lorentzian inner product in so-called Minkowski space, i.e., R^4 = R^(1, 3) with metric signature (1, 3) assumed throughout.

dot product | four-vector | light cone | lightlike | Lorentzian inner product | Lorentzian space | metric signature | Minkowski space | negative lightlike | negative timelike | norm | positive lightlike | positive timelike | spacelike | timelike