A Combinatorial Perspective on Quantum Field Theory

Part I. Preliminaries

1. Introduction
Karen Yeats

2. Quantum Field Theory Set Up
Karen Yeats

3. Combinatorial Classes and Rooted Trees
Karen Yeats

4. The Connes-Kreimer Hopf Algebra
Karen Yeats

5. Feynman Graphs
Karen Yeats

Part II. Dyson-Schwinger Equations

6. Introduction to Dyson-Schwinger Equations
Karen Yeats

7. Sub-Hopf Algebras from Dyson-Schwinger Equations
Karen Yeats

8. Tree Factorial and Leading Log Toys
Karen Yeats

9. Chord Diagram Expansions
Karen Yeats

10. Differential Equations and the (Next-To) {}^{m}




m



Leading Log Expansion
Karen Yeats

Part III. Feynman Periods

11. Feynman Integrals and Feynman Periods
Karen Yeats

12. Period Preserving Graph Symmetries
Karen Yeats

13. An Invariant with These Symmetries
Karen Yeats

14. Weight
Karen Yeats

15. The c_2



c
2



Invariant
Karen Yeats

16. Combinatorial Aspects of Some Integration Algorithms
Karen Yeats

Keywords: Physics, Quantum Field Theories, String Theory, Mathematical Physics, Discrete Mathematics