Derivation of the Lamb Shift using an Effective Field Theory

We rederive the $O(\alpha^5)$ shift of the hydrogen levels in the non-recoil ($m_e/m_P \to 0$) limit using Nonrelativistic QED (NRQED), an effective field theory developed by Caswell and Lepage (Phys. Lett. 167B, 437 (1986)). Our result contains the Lamb shift as a special case. Our calculation is far simpler than traditional approaches and has the advantage of being systematic. It also clearly illustrates the need to renormalize (or ``match'') the coefficients of the effective theory beyond tree level.Comment: 15 pages, 11 Postscript figures, uses Latex2e and epsf.te

Promoting information literacy through a student video contest

This presentation discusses the concept of user-generated content and fansourcing/crowdsourcing, using a video contest, to encourage student participation in the area of information literacy and library instruction. The activity can be a strategy to position the library within campus life and offers an opportunity for constructivist learning

Enumeration of N-rooted maps using quantum field theory

A one-to-one correspondence is proved between the N-rooted ribbon graphs, or maps, with e edges and the (e-N+1)-loop Feynman diagrams of a certain quantum field theory. This result is used to obtain explicit expressions and relations for the generating functions of N-rooted maps and for the numbers of N-rooted maps with a given number of edges using the path integral approach applied to the corresponding quantum field theory.Comment: 27 pages, 7 figure

Feynman diagrams, ribbon graphs, and topological recursion of Eynard-Orantin

We consider two seemingly unrelated problems, the calculation of the WKB expansion of the harmonic oscillator wave functions and the counting the number of Feynman diagrams in QED or in many-body physics and show that their solutions are both encoded in a single enumerative problem, the calculation of the number of certain types of ribbon graphs. In turn, the numbers of such ribbon graphs as a function of the number of their vertices and edges can be determined recursively through the application of the topological recursion of Eynard-Orantin to the algebraic curve encoded in the Schr\"odinger equation of the harmonic oscillator. We show how the numbers of these ribbon graphs can be written down in closed form for any given number of vertices and edges. We use these numbers to obtain a formula for the number of N-rooted ribbon graphs with e edges, which is the same as the number of Feynman diagrams for 2N-point function with e+1-N loops.Comment: 29 pages, 7 figure