Möller, Jan: Fully massive tadpoles at 5-loop : reduction and difference equations. 2012
Inhalt
- Preface
- Introduction and Motivation
- In a Nutshell: Massive Tadpoles, Recurrence Relations and Difference Equations
- Quantum Chromodynamics and Yang-Mills Theory
- Renormalization, Beta-function and Anomalous Dimensions
- Computation of Anomalous Dimensions: Infrared Rearrangement
- Thermal Field Theory: QCD at High Temperature
- Reduction Methods for Feynman Integrals
- Definitions and Notations
- The Integration-by-Parts and Lorentz-invariance Identities
- Feynman Graph Polynomials
- Space-time Dimensional Relations
- Generalized Recurrence Relations
- Solving the System of Identities: The Laporta Algorithm
- Propagators, Sectors and Integrals
- Linear Shifting of Internal Momenta: Sector Relations and Symmetries
- Different Point of View: Identities among Feynman Integrals in r-s Space
- The Laporta Algorithm and an Unique Ordering of Feynman integrals
- Generalized Recurrence Relations: The Advantages and Consequences
- Massive Tadpoles up to the 5-loop Level: Reduction, Master Integrals and Difference Equations
- Notations and Momenta Conventions
- Topologies, Generalized Recurrence Relations, Sector Relations and Symmetries
- Implementation of the Laporta Algorithm in the Computer Algebra System FORM
- Public Implementations and Software: An Overview
- Implementing the Algorithm in FORM
- Adapting the Implementation to Derive Difference Equations
- Reduction: Master Integrals, Bottlenecks, Results
- Solving the System of Difference Equations by Means of Factorial Series
- General Introduction and Definitions
- Solving the Difference Equation via Factorial Series
- The Factorial Series and Boole's Operators
- Solution of Homogeneous and Nonhomogeneous Difference Equation
- Determine Arbitrary Constants: Large-x Behavior
- Numerical Evaluation of Factorial Series
- Application to Fully Massive Tadpoles up to 5-loop
- Summary and Concluding Remarks
- Appendix
- Bibliography
- Acknowledgements
- Eigenständigkeitserklärung