GRMS or Graphical Representation of Model Spaces: Vol. 1 Basics

Przednia okładka
Springer Science & Business Media, 6 gru 2012 - 189
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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Spis treści

Introducing graphical representation
S adapted graphs in different forms
isadapted graphs
i S adapted graphs
Sadapted graphs
i Sadapted graphs
j fadapted graphs
Visualization of restricted model spaces
Physical intuitions and graphs
Mathematical remarks
Graphs and computers
Matrix elements in model spaces
Examples of operators in E basis
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