This expression can be derived directly from the field theory as the vacuum expectation value of the time-ordered product of the free scalar field, that is, the product always taken such that the time ordering of the spacetime points is the same, G F ( x − − y ) = − − i ⟨ ⟨ 0 | T ( Φ Φ ( x ) Φ Φ ( y ) ) | 0 ⟩ ⟩ = − − i ⟨ 0 | [ Θ Θ ( x 0 − − y 0 ) Φ Φ ( x ) Φ Φ ( y ) + Θ Θ ( y 0 − − x 0 ) Φ Φ ( y ) Φ Φ ( x ) ] | 0 ⟩ .