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
11
S adapted graphs in different forms
18
isadapted graphs
30
i S adapted graphs
37
Sadapted graphs
44
i Sadapted graphs
52
j fadapted graphs
66
Visualization of restricted model spaces
74
Physical intuitions and graphs
80
Mathematical remarks
90
Graphs and computers
96
Matrix elements in model spaces
102
Examples of operators in E basis
108
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