path-ordering

In theoretical physics, path-ordering is the procedure (or a meta-operator \mathcal P) that orders a product of operators according to the value of a chosen parameter: \mathcal P \left\{O_1(\sigma_1) O_2(\sigma_2) \cdots O_N(\sigma_N)\right\} \equiv O_{p_1}(\sigma_{p_1}) O_{p_2}(\sigma_{p_2}) \cdots O_{p_N}(\sigma_{p_N}).

Here p is a permutation that orders the parameters by value: p : \{1, 2, \dots, N\} \to \{1, 2, \dots, N\} \sigma_{p_1} \leq \sigma_{p_2} \leq \cdots \leq \sigma_{p_N}.