Bogoliubov causality condition is a causality condition for scattering matrix (S-matrix) in axiomatic quantum field theory. The condition was introduced in axiomatic quantum field theory by Nikolay Bogolyubov in 1955.
In axiomatic quantum theory, S-matrix is considered as a functional of a function [math]\displaystyle{ g: M\to [0,1] }[/math] defined on the Minkowski space [math]\displaystyle{ M }[/math]. This function characterizes the intensity of the interaction in different space-time regions: the value [math]\displaystyle{ g(x)=0 }[/math] at a point [math]\displaystyle{ x }[/math] corresponds to the absence of interaction in [math]\displaystyle{ x }[/math], [math]\displaystyle{ g(x)=1 }[/math] corresponds to the most intense interaction, and values between 0 and 1 correspond to incomplete interaction at [math]\displaystyle{ x }[/math]. For two points [math]\displaystyle{ x,y\in M }[/math], the notation [math]\displaystyle{ x\le y }[/math] means that [math]\displaystyle{ x }[/math] causally precedes [math]\displaystyle{ y }[/math].