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

{{framebox|blue}}Let <math>S(g)</math> be scattering matrix as a functional of <math>g</math>. The Bogoliubov causality condition in terms of variational derivatives has the form:
:::<math>\frac{\delta}{\delta g(x)}\left(\frac{\delta S(g)}{\delta g(y)} S^\dagger(g)\right)=0 \mbox{ for } x\le y. </math>{{frame-footer}}

== 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}}.

[[Category:Quantum field theory]]

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