The Green function with a single pair of arguments ( n = 1 ) is referred to as the two-point function, or propagator. In the presence of both spatial and temporal translational symmetry, it depends only on the difference of its arguments. Taking the Fourier transform with respect to both space and time gives G ( x τ τ ∣ ∣ x ′ τ τ ′ ) = ∫ ∫ k d k 1 β β ∑ ∑ ω ω n G ( k , ω ω n ) e i k ⋅ ⋅ ( x − − x ′ ) − − i ω ω n ( τ τ − − τ τ ′ ) , where the sum is over the appropriate Matsubara frequencies (and the integral involves an implicit factor of ( L / 2 π π ) d , as usual).