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 g: M\to ,1/math> defined on the Minkowski space $M$. This function characterizes the intensity of the interaction in different space-time regions: the value $g(x)=0$ at a point $x$ corresponds to the absence of interaction in $x$, $g(x)=1$ corresponds to the most intense interaction, and values between 0 and 1 correspond to incomplete interaction at $x$. For two points $x,y\in M$, the notation $x\le y$ means that $x$ causally precedes $y$.

Let $S(g)$ be scattering matrix as a functional of $g$. The Bogoliubov causality condition in terms of variational derivatives has the form:
:::$\frac\left(\frac S^\dagger(g)\right)=0 \mbox x\le y.$

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 olland Boston. . .

Axiomatic quantum field theory
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