Bogoliubov causality condition

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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[edit]

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[edit]

  • 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.