Bogoliubov causality condition


Bogoliubov causality condition is a causality condition for scattering matrix in axiomatic quantum field theory. The condition was introduced in axiomatic quantum field theory by Nikolay Bogolyubov in 1955.

Formulation

In axiomatic quantum theory, S-matrix is considered as a functional of a function defined on the Minkowski space. This function characterizes the intensity of the interaction in different space-time regions: the value at a point corresponds to the absence of interaction in, corresponds to the most intense interaction, and values between 0 and 1 correspond to incomplete interaction at. For two points, the notation means that causally precedes.
Let be scattering matrix as a functional of. The Bogoliubov causality condition in terms of variational derivatives has the form: