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Graphical Representation of SUSY and Application to QFT

SUSY2007 @Karlsruhe Univ. 07.7.26. Graphical Representation of SUSY and Application to QFT. S. Ichinose Univ. of Shizuoka, SFNS, Japan. Based on hep-th/0603214,0603220. Sec.1 Introduction. How to denote a mathematical (physical) quantity often affects the understanding of its meaning.

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Graphical Representation of SUSY and Application to QFT

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  1. SUSY2007 @Karlsruhe Univ. 07.7.26 Graphical Representation of SUSY and Application to QFT S. Ichinose Univ. of Shizuoka, SFNS, Japan Based on hep-th/0603214,0603220

  2. Sec.1Introduction How to denote a mathematical (physical) quantity often affectsthe understanding of its meaning Ex. AVector Analysis Ex. BDifferential Form

  3. Ex.C Penrose’s spinor notation (‘71)

  4. Riemann Tensor Ex. D Graph. Rep. of Riemann Tensor (S.I. ‘95) Generally, as the No of suffixes increases, the suffix-free notation is technically advantageous.

  5. RRR-invariants 1(on-shell vanishing)

  6. RRR-invariants2

  7. New Off-shell Relations

  8. Sec.2 Spinor (Weyl Fermion) Complex conj. SL(2,C) dual, suffix up-down

  9. Sigma Matrices 2 by 2 Hermite matrices Connection between chiral world and space-time (vector) world

  10. Spinor Suffix Contraction Wedge structure

  11. Lorenz Vector Double wedge structure

  12. Derivatives of Fermions

  13. Sec.3 Graph Relations Fierz Identity

  14. 2sigma’s

  15. 3sigma’s

  16. Sec.4 Graph Indices Advantage 0. We are free from suffixes Advantage 1. We can calculate using Graphical Relations Advantage 2. Graphs are identified by their Graph Indices Left Chiral Number, Right Chiral Number Left Up-Down Number, Right Up-Down Number Left Wedge Number, Right Wedge Number Dotted Line Number

  17. Indices of SQED

  18. Classification of 2 Sigma’s

  19. Sec.5 Further Extension Non Abelian Higher dimension

  20. Gravitational theory vier-bein Rarita-Schwinger

  21. Sec.6Input-Output Sample Input

  22. Output

  23. Final Output

  24. Sec.6 Conclusion We report the present status of Graphical Representation of SUSY. Outline is finished. However it still needs further development of programming for the ‘public’ use. G O A L

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