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Bogoliubov Axioms, Bogoliubov Reconstruction and Hopf Algebra of Diagrams


Key words :
Bogoliubov Resconstruction, Merge operation (of S-matrix functional),
Bogoliubov Group, Asimptotic Completnes, Osterwalder -Schrader
reconstruction theorem, Asymptotic completnes, constructiv mathematics.

Resume:

In the present paper we suggest to chsnge Ostervalder --- Shrader axioms and
correspondindg reconstruction theorem for Wightman Fields by The Bogoliubov-
Parasiuk R-operation and Corresponding Reconstruction of S-matrix by lagrangian
according Bohr correspondence principa

Each theory of quantum delocalizated objects, such fields must contain the following two structures,
corresponding to their algebraic-observable and dynamical-group properties. Moreover the dynamical
-group structure must respest the algebraic-observable structure that leads to bialgebras....

I the present paper we try to clurify how the Bogoliubov axioms lead to the Hopf
Algebra of Feynman Graps suggested by Connes and Creimer.

We start from the following point: As a algebraic-operator structure we try the
(operater) product of Wick Monomials and as group-dynamical operation the
merge operation of Bogoliubov S-matrix functional. Then we discuss how and why
thes two operation are well-adopted to each-other and try to obtain the Bogoliubov
Group and Hopf Algebra of diagrams (Its diagramm decomposition) by chain
of someat most prime deformation of this definition. At each step we try to
clarify the corresponding categorical properties and the property of this
research at each step wil be the property of well-adopt of this
two structures to each-other..

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