GRMS or Graphical Representation of Model Spaces

1. Front Matter

   Pages N2-V

   PDF

2. Preface

   1. Preface

      • W. Duch

      Pages 1-3

3. Introduction

   1. Introduction

      • W. Duch

      Pages 4-9

4. Architecture of Model Spaces

   1. Front Matter

      Pages 10-10

      PDF

   2. Introducing graphical representation

      • W. Duch

      Pages 11-13

   3. Labeling and ordering the paths

      • W. Duch

      Pages 14-17

   4. Ŝz—adapted graphs in different forms

      • W. Duch

      Pages 18-28

   5. L̂z—adapted graphs

      • W. Duch

      Pages 29-36

   6. (L̂z,Ŝz)—adapted graphs

      • W. Duch

      Pages 37-43

   7. Ŝ2—adapted graphs

      • W. Duch

      Pages 44-51

   8. (L̂z,Ŝ2)—adapted graphs

      • W. Duch

      Pages 52-56

   9. (L̂2,Ŝ2)—adapted graphs

      • W. Duch

      Pages 57-63

   10. (Ĵ2,T̂2)—adapted graphs

       • W. Duch

       Pages 64-66

   11. Spatial symmetry in the graph

       • W. Duch

       Pages 67-73

   12. Visualization of restricted model spaces

       • W. Duch

       Pages 74-79

   13. Physical intuitions and graphs

       • W. Duch

       Pages 80-89

   14. Mathematical remarks

       • W. Duch

       Pages 90-95

   15. Graphs and computers

       • W. Duch

       Pages 96-97

   16. Summary and open problems

       • W. Duch

       Pages 98-100

5. Matrix Elements and Graphs

   1. Front Matter

      Pages 101-101

      PDF

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.

• RMS
• classification
• element
• many-body problem
• mechanics
• mutation
• physics
• quantum mechanics
• quantum physics
• quantum theory
• scattering
• spin
• symmetry

• Max-Planck-Institut für Physik und Astrophysik, Garching bei München, Deutschland

  W. Duch

• Instytut Fizyki, UMK, Toruń, Poland

  W. Duch

Policies and ethics