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

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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:
 

References

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  • 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.