Path-ordering
In theoretical physics, path-ordering is the procedure (or a meta-operator P {\displaystyle {\mathcal {P}}} ) that orders a product of operators according to the value of a chosen parameter: P { O 1 ( σ 1 ) O 2 ( σ 2 ) ⋯ O N ( σ N ) } ≡ O p 1 ( σ p 1 ) O p 2 ( σ p 2 ) ⋯ O p N ( σ p N ) . {\displaystyle {\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 , … , N } → { 1 , 2 , … , N } {\displaystyle p:\{1,2,\dots ,N\}\to \{1,2,\dots ,N\}} σ p 1 ≤ σ p 2 ≤ ⋯ ≤ σ p N .