The purpose of these notes is to give some simple tools and
pictures to physicists and ' chemists working on the many-body
problem. Abstract thinking and seeing have much in common - we say
"I see" meaning "I understand" , for example. Most of us prefer to
have a picture of an abstract object. The remarkable popularity of
the Feynman diagrams, and other diagrammatic approaches to
many-body problem derived thereof, may be partially due to this
preference. Yet, paradoxically, the concept of a linear space, as
fundamental to quantum physics as it is, has never been cast in a
graphical form. We know that is a high-order contribution to a
two-particle scattering process (this one invented by
Cvitanovic(1984)) corresponding to a complicated matrix element.
The lines in such diagrams are labeled by indices of
single-particle states. When things get complicated at this level
it should be good to take a global view from the perspective of the
whole many-particle space. But how to visualize the space of all
many-particle states ? Methods of such visualization or graphical
representation of the ,spaces of interest to physicists and
chemists are the main topic of this work.
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