Calculation of Momentum Space Integrals

The following sections are included:

• Simple Loop Integrals

  • Expansion of Loop Function

  • Modified MS-Scheme and Various Redefinitions of Mass Scale

  • Further Subtraction Schemes

• Classification of Diagrams

• Five-Loop Diagrams

• Reduction Algorithm based on Partial Integration

  • Triangle Diagram

  • General Triangle Rule

  • Reduction Algorithms

• Method of Ideal Index Constellations in Configuration Space

  • Dual Diagrams

  • Star-Triangle Rule for an Ideal Vertex

  • One Step from Ideal Index Constellation

  • Transformation of Indices

  • Construction of Tables

• Special Treatment of Generic Four- and Five-Loop Diagrams

  • N-Shaped Diagram

• Computer-Algebraic Program

• Appendix 13A Fourier Transformation of Simple Powers in D Dimensions

• Appendix 13B Further Expansions of Gamma Function

• Notes and References