Physics, Lagrangian, Symmetry, Classical Mechanics, Mechanics.
the x’ᵢⱼ and xᵢⱼterms is to show which particle we are referring to, while the second one in x’ᵢⱼ and xᵢⱼand the first in ϵⱼ indicates which component of the vector we are concerned with. Since ϵ is the vector that all of the particles have been translated by, the displacement vectors between all