The integral over the Schwinger parameters u i can be split up as before into an integral over the total proper time u = u 0 + u 1 ... + u n and an integral over the fraction of the proper time in all but the first segment of the loop v i = ⁠ u i / u ⁠ for i ∈ {1,2,..., n }. The v i are positive and add up to less than 1, so that the v integral is over an n -dimensional simplex.