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Bogoliubov causality condition
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Bogoliubov causality condition : ウィキペディア英語版
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 () 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.

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