Evaluating Feynman integrals /
Saved in:
| Author / Creator: | Smirnov, V. A. (Vladimir Alexandrovich), 1951- |
|---|---|
| Imprint: | Berlin : Springer, 2004. |
| Description: | ix, 244 p. : ill. ; 25 cm. |
| Language: | English |
| Series: | Springer tracts in modern physics, 0081-3869 ; v. 211 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/5548591 |
Table of Contents:
- 1. Introduction
- 1.1. Notation
- References
- 2. Feynman Integrals: Basic Definitions and Tools
- 2.1. Feynman Rules and Feynman Integrals
- 2.2. Divergences
- 2.3. Alpha Representation
- 2.4. Regularization
- 2.5. Properties of Dimensionally Regularized Feynman Integrals
- References
- 3. Evaluating by Alpha and Feynman Parameters
- 3.1. Simple One- and Two-Loop Formulae
- 3.2. Auxiliary Tricks
- 3.2.1. Recursively One-Loop Feynman Integrals
- 3.2.2. Partial Fractions
- 3.2.3. Dealing with Numerators
- 3.3. One-Loop Examples
- 3.4. Feynman Parameters
- 3.5. Two-Loop Examples
- References
- 4. Evaluating by MB Representation
- 4.1. One-Loop Examples
- 4.2. Multiple MB Integrals
- 4.3. More One-Loop Examples
- 4.4. Two-Loop Massless Examples
- 4.5. Two-Loop Massive Examples
- 4.6. Three-Loop Examples
- 4.7. More Loops
- 4.8. MB Representation versus Expansion by Regions
- 4.9. Conclusion
- References
- 5. IBP and Reduction to Master Integrals
- 5.1. One-Loop Examples
- 5.2. Two-Loop Examples
- 5.3. Reduction of On-Shell Massless Double Boxes
- 5.4. Conclusion
- References
- 6. Reduction to Master Integrals by Baikov's Method
- 6.1. Basic Parametric Representation
- 6.2. Constructing Coefficient Functions. Simple Examples
- 6.3. General Recipes. Complicated Examples
- 6.4. Two-Loop Feynman Integrals for the Heavy Quark Potential
- 6.5. Conclusion
- References
- 7. Evaluation by Differential Equations
- 7.1. One-Loop Examples
- 7.2. Two-Loop Example
- 7.3. Conclusion
- References
- A. Tables
- A.1. Table of Integrals
- A.2. Some Useful Formulae
- B. Some Special Functions
- References
- C. Summation Formulae
- C.1. Some Number Series
- C.2. Power Series of Levels 3 and 4 in Terms of Polylogarithms
- C.3. Inverse Binomial Power Series up to Level 4
- C.4. Power Series of Levels 5 and 6 in Terms of HPL
- References
- D. Table of MB Integrals
- D.1. MB Integrals with Four Gamma Functions
- D.2. MB Integrals with Six Gamma Functions
- E. Analysis of Convergence and Sector Decompositions
- E.1. Analysis of Convergence
- E.2. Practical Sector Decompositions
- References
- F. A Brief Review of Some Other Methods
- F.1. Dispersion Integrals
- F.2. Gegenbauer Polynomial x-Space Technique
- F.3. Gluing
- F.4. Star-Triangle Relations
- F.5. IR Rearrangement and R *
- F.6. Difference Equations
- F.7. Experimental Mathematics and PSLQ
- References
- List of Symbols
- Index
