# Bogoliubov causality condition

**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.

## 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 .

Template:FrameboxLet be scattering matrix as a functional of . The Bogoliubov causality condition in terms of variational derivatives has the form:

## References

- N. N. Bogoliubov, A. A. Logunov, I. T. Todorov (1975):
*Introduction to Axiomatic Quantum Field Theory*. Reading, Mass.: W. A. Benjamin, Advanced Book Program. - N. N. Bogoliubov, A. A. Logunov, A. I. Oksak, I. T. Todorov (1990):
*General Principles of Quantum Field Theory*. Kluwer Academic Publishers, Dordrecht [Holland]; Boston. ISBN 0-7923-0540-X. ISBN 978-0-7923-0540-8.